According to 2013 report from Population Reference Bureau, the mean travel time to work of workers ages 16 and older who did not work at home was 30.7 minutes for NJ State with a standard deviation of 23 minutes. Assume the population is normally distributed.

Required:
a. If a worker is selected at random, what is the probability that his travel time to work is less than 30 minutes?
b. Specify the mean and the standard deviation of the sampling distribution of the sample means, for samples of size 36.
c. What is the probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes?

Answers

Answer 1

Answer:

a) 48.80% probability that his travel time to work is less than 30 minutes

b) The mean is 30.7 minutes and the standard deviation is of 3.83 minutes.

c) 13.13% probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 30.7, \sigma = 23[/tex]

a. If a worker is selected at random, what is the probability that his travel time to work is less than 30 minutes?

This is the pvlaue of Z when X = 30. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{30 - 30.7}{23}[/tex]

[tex]Z = -0.03[/tex]

[tex]Z = -0.03[/tex] has a pvalue of 0.4880.

48.80% probability that his travel time to work is less than 30 minutes

b. Specify the mean and the standard deviation of the sampling distribution of the sample means, for samples of size 36.

[tex]n = 36[/tex]

Applying the Central Limit Theorem, the mean is 30.7 minutes and the standard deviation is [tex]s = \frac{23}{\sqrt{36}} = 3.83[/tex]

c. What is the probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes?

This is 1 subtracted by the pvalue of Z when X = 35. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{35 - 30.7}{3.83}[/tex]

[tex]Z = 1.12[/tex]

[tex]Z = 1.12[/tex] has a pvalue of 0.8687

1 - 0.8687 = 0.1313

13.13% probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes


Related Questions

Multiply 6.7 x 104 times 4.8 x 106 by using scientific notation. Round your answer to one decimal place in scientific notation with no spaces.

Answers

Answer:

3.216×[tex]10^{11}[/tex]

Step-by-step explanation:

I'm assuming 104 is [tex]10^{4}[/tex] and 106 is [tex]10^{6}[/tex].

6.7×[tex]10^{4}[/tex]×4.8×[tex]10^{6}[/tex]=

32.16×[tex]10^{10}[/tex]=

3.216×[tex]10^{11}[/tex]

Our answer is 3.216×[tex]10^{11}[/tex].

11 — 9y = — 6у +8
solve for y
pleaseee

Answers

Answer:

-The value of [tex]y[/tex]:

[tex]y = 1[/tex]

Step-by-step explanation:

-Find the value of [tex]y[/tex]:

[tex]11- 9y = -6y + 8[/tex]

-Add both sides by [tex]6y[/tex] and combine [tex]9y[/tex] and [tex]6y[/tex] together:

[tex]11- 9y + 6y = -6y + 6y+ 8[/tex]

[tex]11 - 3y = 8[/tex]

-Subtract both sides by [tex]11[/tex]:

[tex]11 - 11 - 3y = 8 -11[/tex]

[tex]-3y = -3[/tex]

-Divide both sides by [tex]-3[/tex]:

[tex]\frac{-3y}{-3} = \frac{-3}{-3}[/tex]

[tex]y = 1[/tex]

So the final answer is [tex]y = 1[/tex] .

A contractor developed a multiplicative time-series model to forecast the number of contracts in future quarters, using quarterly data on number of contracts during the 3-year period from 2010 to 2012. The following is the resulting regression equation: ln = 3.37 + 0.117 X - 0.083 Q1 + 1.28 Q2 + 0.617 Q3 where is the estimated number of contracts in a quarter X is the coded quarterly value with X = 0 in the first quarter of 2010 Q1 is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise Q2 is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise Q3 is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise Using the regression equation, which of the following values is the best forecast for the number of contracts in the third quarter of 2013?A. The quarterly growth rate in the number of contracts is significantly different from 100% (? = 0.05).
B. The quarterly growth rate in the number of contracts is not significantly different from 0% (? = 0.05).
C. The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05).
D. The quarterly growth rate in the number of contracts is not significantly different from 100% (? = 0.05).

Answers

There is a missing content in the question.

After the statements and before the the options given; there is an omitted content which says:

Referring to Table 16-5, in testing the coefficient of X in the regression equation (0.117) the results were a t-statistic of 9.08 and an associated p-value of 0.0000. Which of the following is the best interpretation of this result?

Answer:

C. The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05).

Step-by-step explanation:

From the given question:

The resulting regression equation can be represented as:

[tex]\hat Y = 3.37 + 0.117 X - 0.083 Q_1 + 1.28 Q_2 + 0.617Q_3[/tex]

where;

the estimated number of contracts in a quarter X is the coded quarterly value with X = 0

the first quarter of 2010 Q1 is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise

Q2 is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise

Q3 is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise

Our null and alternative hypothesis can be stated as;

Null hypothesis :

[tex]H_0 :[/tex]  The quarterly growth rate in the number of contracts is not  significantly different from 0% (? = 0.05)

[tex]H_a:[/tex]  The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05)

The decision rule is to reject the null hypothesis if the p-value is less than 0.05.

From the missing omitted part we added above; we can see that the   t-statistics value = 9.08 and the p-value = 0.000 .

Conclusion:

Thus; we reject the null hypothesis and accept the alternative hypothesis. i.e

The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05)

Which statement describes the graph of the system of equations?

Answers

Answer:

Are there any choices?..

The correct statement the describes the equation is The lines intersect at (1, 0) and the lines are parallel.

x - y = 1.............equation 1

y - x = 1.............equation 2

Add equations (1) and (2):

(x - y) + (y - x) = 1 + 1

Simplifying

0 = 2

Since 0 = 2, the system is inconsistent, meaning there is no solution. The lines represented by the equations are parallel and will never intersect.

The system of equations has no solution, as the lines represented by the equations are parallel and will never intersect.

learn more about parallel here

brainly.com/question/17405097

#SPJ2

The complete question is- Which statement describes the graph of the system of equations?

[x-y=1

Ly- X= 1

The lines are parallel.

The lines are coinciding.

The lines intersect at(1, 0).

The lines intersect at (-1,0).

Question: A box contains 160 Iphone XR's.
60% of the IPhones are Forest Green.
How many IPhones are Forest Green?

Answers

Answer:

96

Step-by-step explanation:

60% * 160 = 0.6 * 160 = 96.

Answer:

None

Step-by-step explanation:

There is no Forest Green iPhone XR's only the 11 Pros have that color.

A sports physician conducts an observational study to learn the average amount of time that 3,000 swimmers in the town can hold their breath underwater. He uses 150 sampling of 60 people. The average of the means of all the samplings is 72.7, and the standard deviation is 0.92. This is a histogram of the sampling distribution of the sample mean

Answers

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

A sports physician conducts an observational study to learn the average amount of time that 3,000 swimmers in the town can hold their breath underwater. He uses 150 sampling of 60 people. The average of the means of all the samplings is 72.7, and the standard deviation is 0.92. This is a histogram of the sampling distribution of the sample mean. Based on this data, with a 95% confidence interval the researchers can determine that the actual average amount of time the entire population can hold their breath under water is?

Given Information:

sample mean time = 72.7

sample standard deviation = 0.92

Sampling size = n = 150

Confidence level = 95%

Required Information:

95% confidence interval = ?  

Answer:

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 72.7 \pm 0.14836\\\\\text {confidence interval} = 72.7 - 0.14836, \: 72.7 + 0.14836\\\\\text {confidence interval} = (72.552, \: 72.848)\\\\[/tex]

Step-by-step explanation:

The confidence interval is given by

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\[/tex]

Where [tex]\bar{x}[/tex] is the sample mean time and Margin of error is given by

[tex]$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\[/tex]

Where n is the sampling size, s is the sample standard deviation, and [tex]t_{\alpha/2}[/tex] is the t-score corresponding to 95% confidence level.

The t-score corresponding to 95% confidence level is

Significance level = 1 - 0.95 = 0.05/2 = 0.025

Degree of freedom = n - 1 = 150 - 1 = 149

From the t-table at α = 0.025 and DoF = 149

t-score = 1.975

[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 1.975\cdot \frac{0.92}{\sqrt{150} } \\\\MoE = 1.96\cdot 0.07512\\\\MoE = 0.14836\\\\[/tex]

So the required 95% confidence interval is

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 72.7 \pm 0.14836\\\\\text {confidence interval} = 72.7 - 0.14836, \: 72.7 + 0.14836\\\\\text {confidence interval} = (72.552, \: 72.848)\\\\[/tex]

Therefore, we are 95% confident that actual average amount of time the entire population can hold their breath under water is within the range of (72.552, 72.848)

Answer the inequality

Answers

Answer:

A.

Step-by-step explanation:

Add 4:

-5x ≤ 10

Divide by -5:

x ≥ -2

The loaves of rye bread distributed to a local store by a certain bakery have an average length of 30 centimeters and a standard deviation of 2 centimeters. Assuming the lengths are normally distributed. What percentage of loaves are between 26.94 and 32.18 centimeters

Answers

Answer:

79.91% of loaves are between 26.94 and 32.18 centimeters

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 30, \sigma = 2[/tex]

What percentage of loaves are between 26.94 and 32.18 centimeters

This is the pvalue of Z when X = 32.18 subtracted by the pvalue of Z when X = 26.94.

X = 32.18:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{32.18 - 30}{2}[/tex]

[tex]Z = 1.09[/tex]

[tex]Z = 1.09[/tex] has a pvalue of 0.8621

X = 26.94:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{26.94 - 30}{2}[/tex]

[tex]Z = -1.53[/tex]

[tex]Z = -1.53[/tex] has a pvalue of 0.0630

0.8621 - 0.0630 = 0.7991

79.91% of loaves are between 26.94 and 32.18 centimeters

What is the missing number in the pattern? Please Help. Been stuck on this for hours.

Answers

Answer:

8

Step-by-step explanation:

The other patterns go with the two factors on top (2 x 3 = 6 and 3 x 3 = 9).

So, 2 x 4 = 8

Draw a model of square root of 12 using perfect squares

Answers

Answer:

The answer is "[tex]\sqrt{12}[/tex] is not a perfect square".

Step-by-step explanation:

12 is not a perfect square because it is the natural number, and no other natural number would square the number 12, that's why it is not a perfect square.

If we calculate the square root of [tex]\sqrt{12}[/tex]. so, it is will give [tex]2\sqrt{3}[/tex] that is not a perfect square root which can be described as follows:

[tex]\Rightarrow \sqrt{12}= \sqrt{2\times 2\times 3}[/tex]

            [tex]= \sqrt{2^2\times 3}\\\\= 2\sqrt{3}\\\\[/tex]

[tex]\bold{\sqrt{12}}[/tex] is not a perfect square root.

Answer:

Here's a picture

Step-by-step explanation:

what is the value of x in the equation 2x+3y=36 when y=6​

Answers

Answer:

9

Step-by-step explanation:

[tex]2x+3y=36\\\\2x+3(6)=36\\\\2x+18=36\\\\2x=18\\\\x=9[/tex]

Hope this helps!

Answer:

X= 9

Step-by-step explanation:

2x+3y=36

2x+3(6)=36

2x+18=36

    -18  -18

2x=18

----------

   2

x=9

Which of the following is(are) the solution(s) to | x-1|-8?
A. X= 7.-9
B. X = 9
C. X = -79
D. X = 7

Answers

Answer:

Step-by-step explanation:

|x-1|=8

if (x-1) >= 0 meaning x >= 1

then |x-1| = x-1

and then the solution of the equation is

x-1=8

<=> x = 9

if (x-1) <= 0 meaning x <= 1

then |x-1| = -(x-1) = -x+1

so the solution of the equation is

-x+1=8

<=> -x = 7

<=> x = -7

so the solutions are -7 and 9

answer C

do no hesitate if you need further explanation

thank you

A public relations firm found that only 27% of voters in a certain state are satisfied with their U.S. senators. How large a sample of voters should be drawn so that the sample proportion of voters who are satisfied with their senators is approximately normally distributed?a) 38b) 14c) 10d) 48

Answers

Answer:

a) 38

Step-by-step explanation:

The normal distribution can be applied if:

[tex]np \geq 5[/tex] and [tex]n(1-p) \geq 5[/tex]

In this question:

[tex]p = 0.27[/tex]

Then

a) 38

n = 38.

Then

38*0.27 = 10.26

38*0.73 = 27.74

Satisfies. But is this the smallest sample of the options which satisfies.

b) 14

n = 14

Then

14*0.23 = 3.22

14*0.77 = 10.78

Does not satisfy

c) 10

Smaller than 14, which also does not satisfy, so 10 does not satisfy.

d) 48

Greater than 38, which already satisfies. So the answer is a)

Data on U.S, Work-Related fatalities by cause follow (The World Almanac,2012)Cause of Fatality Number of Fatalities Transportation Incidents 1795 Assaults and violent acts 837 Contacts with objects and equipment 741 Falls 645 Exposure to harmful substances 404 Fires and explosions 113 Assume that a fatality will be randomly chosen from this population. a. What is the probability the fatality resulted froma fall? b. What is the probability the fatality resulted from a transporation incident? c. What cause of fatality is least likely to occur? What is th probability the fatality resulted from this cause?

Answers

Answer:

a) Probability the fatality resulted from a fall = 0.1422

b) Probability the fatality resulted from a transportation incident = 0.3958

c(i) The cause of fatality that is least likely to occur is fatality due to fires and explosions with the lowest number of fatalities, 113.

c(ii) Probability that the fatality resulted from fires and explosions = 0.0249

Step-by-step explanation:

Data on U.S, Work-Related fatalities by cause follow (The World Almanac, 2012)

Cause of Fatality | Number of Fatalities Transportation Incidents | 1795

Assaults and violent acts | 837

Contacts with objects and equipment | 741

Falls | 645

Exposure to harmful substances | 404

Fires and explosions | 113

Total number of fatalities = 1795+837+741+645+404+113 = 4,535

Assume that a fatality will be randomly chosen from this population.

a. What is the probability the fatality resulted from a fall?

The probabilty of an event is given mathematically as the number of elements in that event divided by the Total number of elements in the sample space.

P(E) = n(E) ÷ n(S)

Probability the fatality resulted from a fall = (645/4535) = 0.14223 = 0.1422

b. What is the probability the fatality resulted from a transportation incident?

Probability the fatality resulted from a transportation incident = (1795/4535) = 0.39581 = 0.3958

c(i) What cause of fatality is least likely to occur?

The cause of fatality that is least likely to occur is the cause of fatality with the lowest frequency or number of fatalities. And this is fatality due to fires and explosions with the lowest fatalities of 113

c(ii). What is the probability the fatality resulted from this cause?

This is the probability that the fatality resulted from fires and explosions.

Probability that the fatality resulted from fires and explosions = (113/4535) = 0.02492 = 0.0249

Hope this Helps!!!

10. You just hung a picture twelve inches above the wall trim. Your friend thinks the picture looks
crooked. Use what you know about parallel lines and transversals to determine if the picture is level.
Step 1: You don't have a level, but you are in luck. You know the wall trim is level. You have a
protractor and the sun is casting a shadow on the wall. Describe how you can determine if the picture
is level. (3 points)

Answers

Answer:

The angles measured between the shadow and the wall trim and the shadow and the top or bottom of the picture should be equal if the picture is level

Step-by-step explanation:

Whereby the picture is 12 inches above the wall trim and the Sun is casting a shadow on the wall, therefore, the edges of the shadow of a straight edged object is straight

If the picture is level, the shadow cast by the sun is transversal to the wall trim and the line formed by extending the bottom or top of the picture in the direction of the shadow. That is, if the picture is parallel, the shadow cast by the Sun on the wall is transversal to the picture and the wall trim if or when the shadow eventually crosses the picture

With the protractor, the angle between the shadow and the wall trim and the shadow and the top or bottom is measured

The angles measured should be the same if the picture is level.

The HCF of two numbers is 11, and their L.C.M is 368. If one number is 64, then the other number is ….

Answers

Answer:

63.45

Step-by-step explanation:

First, it should be noted that the question is incorrect because 64 can't be divided by 11 but assuming that the question is correct, the solution is as follows

Given

LCM = 368

HCF = 11

One number = 64

Required

The other number

Let both numbers be represented by m and n, such that

[tex]m = 64[/tex]

From laws of HCF and LCM

The product of both numbers = Product of HCF and LCM

i.e.

[tex]m * n = HCF * LCM[/tex]

By substituting 68 for m; 368 for LCM and 11 for HCF

[tex]m * n = HCF * LCM[/tex] becomes

[tex]64 * n = 368 * 11[/tex]

[tex]64n = 4048[/tex]

Divide both sides by 64

[tex]\frac{64n}{64} = \frac{4048}{64}[/tex]

[tex]n = \frac{4048}{64}[/tex]

[tex]n = 63.25[/tex]

Which equation does not represent a linear function of x?


a. y = -3 over 4 x
b. y = x over 2
c. y = - 3 + 2x
d. y = 3x2 - 2

Answers

The answer is b. y = x over 2

Hallie can use the equation p = 4l + 4w + 4h to determine the sum of the lengths of the edges of a rectangular prism. She begins to solve the equation for h but runs out of time. Her partial work is shown below:
p = 4l + 4w + 4h

= l + w + h
h = –
Which expression should follow the subtraction in Hallie’s equation?

Answers

Answer:

h = p - l - w

Step-by-step explanation:

p = 4l + 4w + 4h       Divide l, w, and h by 4

p = l + w + h              Set the equation equal to h

h = p - l - w

Answer:

A just did it on edge<3

What is the measure of angle 7?

Answers

Answer: 95 degrees

Step-by-step explanation:

We can infer than angles 1, 4, 5, 8 are all equal and angles 2, 3, 6, 7 are also equal to eachother. These two sets of angles are supplementary(you’d get 180 by adding them)

So 3x+10=4x-15

if you rearrange you'll get

x=25

therefore angle 1 equals

3*25+10=85

angle 1 and 7 are supplementary

thus angle 7 equals

180-85=95

PLEASE HELP

In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = (x-2)^2 -3. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).

Answers

Answer:

Step-by-step explanation:

F(x) results in a parabola with vertex (0,0) wich mean there is only one x-int at that point. g(x) has been shifted the grapgh of f(x) to the right by to units and down by three unites. Now our vertex lies in the point (2,-3) and since the graph was move dow i=of the x-axis we now have two different x-intercepts.

please very soon I offer the crown !!! + 10 points urgently !!!

Answers

Answer:

a. 2 groups of 2 is 4

b. 3 groups of 2 is 6

c. 4 groups of 2 is 8

d. 5 groups of 2 is 10

e. 6 groups of 2 is 12

Answer:

a - 2

b- 3

c- 4 groups of 2 is 8

d- 5 groups of 2 is 10

e- 6 groups of 2 is 12

One number is 3 more than 2 times the other, and their sum is 27. Find the numbers.
If x represents the smaller number, then the larger number is
3x + 2
2x + 3
21x + 3)

Answers

Answer:

Option 2 is correct

Step-by-step explanation:

One number is 2 times another number plus 3. Their sum is 21.

"One number is 2 times another number plus 3" translated to

x = smaller number = another number

It is also given that: Their sum is 21.

Combine like terms:

3x+3 = 21

Answer:

I do questions like these everyday so I have too much experience. Let me explain step by step for you.

Brainliest?

First lets set 2 variables x and y

Lets make 2 equations.

x=3+2*y

Thats because it says 'x' is 3 more (+) than 2 times(*) 'y'

Now lets set second, we know both of them add up to 27.

x+y = 27

Since we know what x is equal to (look above equation)

We can replace it.

x is replaced with 3+2*y

3+2y+y = 27

3+4y = 27

Simplify 27-3 = 24

24/4 = 6

Now lets plug in for x

3+2*6 = 15

15 - x

6 - y

:))

g A two-tailed test is one where: Select one: a. results in only one direction can lead to rejection of the null hypothesis b. negative sample means lead to rejection of the null hypothesis c. results in either of two directions can lead to rejection of the null hypothesis d. no results lead to the rejection of the null hypothesis

Answers

Answer:

c. results in either of two directions can lead to rejection of the null hypothesis.

Step-by-step explanation:

A two tailed test is performed when we want to test if there is statistically significant difference from the null state. That means that if the statistic value is significantly higher or significantly lower, we will reject the null hypothesis. Both tails have rejection areas.

In determining automobile-mileage ratings, it was found that the mpg (X) for a certain model is normally distributed, with a mean of 33 mpg and a standard deviation of 1.7 mpg. Find the following:__________.
a. P(X<30)
b. P(28 c. P(X>35)
d. P(X>31)
e. the mileage rating that the upper 5% of cars achieve.

Answers

Answer:

a) P(X < 30) = 0.0392.

b) P(28 < X < 32) = 0.2760

c) P(X > 35) = 0.1190

d) P(X > 31) = 0.8810

e) At least 35.7965 mpg

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 33, \sigma = 1.7[/tex]

a. P(X<30)

This is the pvalue of Z when X = 30. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{30 - 33}{1.7}[/tex]

[tex]Z = -1.76[/tex]

[tex]Z = -1.76[/tex] has a pvalue of 0.0392.

Then

P(X < 30) = 0.0392.

b) P(28 < X < 32)

This is the pvalue of Z when X = 32 subtracted by the pvalue of Z when X = 28. So

X = 32

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{32 - 33}{1.7}[/tex]

[tex]Z = -0.59[/tex]

[tex]Z = -0.59[/tex] has a pvalue of 0.2776.

X = 28

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{28 - 33}{1.7}[/tex]

[tex]Z = -2.94[/tex]

[tex]Z = -2.94[/tex] has a pvalue of 0.0016.

0.2776 - 0.0016 = 0.2760.

So

P(28 < X < 32) = 0.2760

c) P(X>35)

This is 1 subtracted by the pvalue of Z when X = 35. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{35 - 33}{1.7}[/tex]

[tex]Z = 1.18[/tex]

[tex]Z = 1.18[/tex] has a pvalue of 0.8810.

1 - 0.8810 = 0.1190

So

P(X > 35) = 0.1190

d. P(X>31)

This is 1 subtracted by the pvalue of Z when X = 31. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{31 - 33}{1.7}[/tex]

[tex]Z = -1.18[/tex]

[tex]Z = -1.18[/tex] has a pvalue of 0.1190.

1 - 0.1190 = 0.8810

So

P(X > 31) = 0.8810

e. the mileage rating that the upper 5% of cars achieve.

At least the 95th percentile.

The 95th percentile is X when Z has a pvalue of 0.95. So it is X when Z = 1.645. Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.645 = \frac{X - 33}{1.7}[/tex]

[tex]X - 33 = 1.645*1.7[/tex]

[tex]X = 35.7965[/tex]

At least 35.7965 mpg

The upper 5% of cars have a mileage rating of 35.805 mpg

What is z score?

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean) / standard deviation

Given;  mean of 33 mpg and a standard deviation of 1.7

a) For < 30:

z = (30 - 33)/1.7 = -1.76

P(x < 30) = P(z < -1.76) = 1 - 0.8413 = 0.0392

b) For < 28:

z = (28 - 33)/1.7 = -2.94

P(x < 28) = P(z < -2.94) = 0.0016

c) For > 35:

z = (35 - 33)/1.7 = 1.18

P(x > 35) = P(z > 1.18) = 1 - P(z < 1.18) = 1 - 0.8810 = 0.119

d) For > 31:

z = (31 - 33)/1.7 = -1.18

P(x > 31) = P(z > -1.18) = 1 - P(z < -1.18) = 0.8810

e) The  upper 5% of cars achieve have a z score of 1.65, hence:

1.65 = (x - 33)/1.7

x = 35.805 mpg

The upper 5% of cars have a mileage rating of 35.805 mpg

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The accompanying data represent the total travel tax (in dollars) for a 3-day business trip in 8 randomly selected cities A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot indicates there are no outliers. Complete parts through below.
68.87 78.25 70.44 84.67 79.79 86.33 100.24 98.26
Click the icon to view the table of critical t-values.
a. Determine a point estimate for the population mean travel tax A point estimate for the population mean travel tax is $ 83.36. (Round to two decimal places as needed.)
b. Construct and interpret a 95% confidence interval for the mean tax paid for a three-day business trip.
Select the correct choice below and fill in the answer boxes to complete your choice. (Round to two decimal places as needed.)
A. The lower bound is $ and the upper bound is $. One can be % confident that all cities have a travel tax between these values.
B. The lower bound is $ and the upper bound is $ The travel tax is between these values for % of all cities.
C. The lower bound is $ and the upper bound is $ There is a % probability that the mean travel tax for all cities is between these values.
D. The lower bound is $ and the upper bound is One can be [95]% confident that the mean travel tax for all cities is between these values.
c. What would you recommend to a researcher who wants to increase the precision of the interval, but does not have access to additional data?
A. The researcher could decrease the level of confidence.
B. The researcher could decrease the sample standard deviation.
C. The researcher could increase the level of confidence.
D. The researcher could increase the sample mean

Answers

Answer:

Step-by-step explanation:

Given that:

68.87, 78.25, 70.44, 84.67, 79.79, 86.33, 100.24, 98.26

we calculate sample mean and standard deviation from given data

Sample Mean

[tex]\bar x = \frac{\sum (x)}{n} =\frac{666.85}{8} \\\\=83.35625[/tex]

Sample Variance

[tex]s^2= \frac{\sum (x- \bar x )^2}{n-1} \\\\=\frac{933.224787}{7} =133.317827[/tex]

sample standard deviation

[tex]s=\sqrt{s^2} \\=\sqrt{133.317827} \\ =11.546334[/tex]

95% CI for [tex]\mu[/tex] using t - dist

Sample mean = 83.35625

Sample standard deviation = 11.546334

Sample size = n = 8

Significance level = α = 1 - 0.95 = 0.05

Degrees of freedom for t - distribution

d-f = n - 1 = 7

Critical value

[tex]t_{\alpha 12, df}= t_{0.025, df=7}=2.365[/tex] ( from t - table , two tails, d.f =7)

Margin of Error

[tex]E = t_{\alpha 12, df}\times \frac{s_x}{\sqrt{n} } \\\\=2.365 \times \frac{11.546334}{\sqrt{8} } \\\\=2.365 \times 4.082246\\\\E=9.654512[/tex]

Limits of 95% Confidence Interval are given by:

Lower limit

[tex]\bar x - E = 83.35625-9.654512\\\\=73.701738\approx 73.702[/tex]

Upper Limit

[tex]= \bar x + E\\=83.35625+ 9.654512\\=93.010762 \approx 93.011[/tex]

95% Confidence interval is

[tex]\bar x \pm E = 83.35625 \pm 9.654512\\\\=(73.701738,93.010762)[/tex]

95% CI using t - dist (73.70 < μ < 93.01)

D. The lower bound is $ and the upper bound is One can be [95]% confident that the mean travel tax for all cities is between these values.

c.What would you recommend to a researcher who wants to increase the precision of the interval, but does not have access to additional data?

A. The researcher could decrease the level of confidence.

A circle with circumference 6 has an arc with a 20 degrees central angle. What is the length of the arc?

Answers

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

So first calculate what fraction of the circumference the arc is.

[tex]\frac{20}{360}=\frac{1}{18}[/tex]

Now the circumference is 6, so one eighteenth of that is [tex]\frac{1}{3}[/tex]

A meteorologist reports that the chance of snow is less

than 30%. The correct inequality to represent this

comparison is s < 30. The variable s represents the

likelihood of snow

Which numbers are solutions of the inequality?

Choose all that apply.

20%

35%

17%

30%

29

%

1.5%

Answers

Answer:

1, 3, 5, 6

Step-by-step explanation:

Your solution has to be less than the number they are giving you for example if you have -3 one solution could be -16

The numbers that are solutions to the inequality are as follows: 20%, 17%, 29.5%, 1.5%.

What are the solutions of the inequality?

The solution of an inequality is the set of all possible values that could serve as the result of the expression. So, for the given problem, the set of values that would correspond to the likelihood of snow is 20%, 17%, 29.5%, and 1.5%.

In other words, these percentages are less than 30% and can be rightly represented by the variable s.

Learn more about inequality here:

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At the kennel, the ratio of cats to dogs is 4:5. There are 27 animals in all. How many cats are in the kennel?

Answers

Answer:

Step-by-step explanation:

4x+5x=27

9x=27

x=27/9

x=3

4x3=12

5x3=15

The total number of cats were 12.

Based on the ratio of dogs to cats in the shelter, we know that out of 27 animals, there are 12 cats.

The ratio of cats to dogs is 4:5 which means that there are 5 dogs for every 4 cats.

This means that out of 9 animals, 4 would be cats and 5 would be dogs. If there was 27 animals therefore:

= 4 / 9 x 27

= 108 / 9

= 12 cats

In conclusion, there are 12 cats.

Find out more at https://brainly.com/question/9723361.

Making Friends Online
A survey conducted in March 2015 asked 1060 teens to estimate, on average, the number of friends they had made online. while 43% had not made any friends online, a small number of the teens had made many friends online.
(a) Do you expect the distribution of number of friends made online to be symmetric, skewed to the right, or skewed to the left?
Skewed to the left.
Symmetric
Skewed to the right.
(b) Two measures of center for this distribution are 1 friend and 5.3 friends. Which is most likely to be the mean and which is most likely to be the median?
Mean=
Median=
1Lenhart A, "Teens, Technology, and Friendships", Pew Research Center, pewresearch.org, August 6, 2015. Value for the mean is estimated from information given.

Answers

Answer:

Step-by-step explanation:

) Do you expect the distribution of number of friends made online to be symmetric, skewed to the right, or skewed to the left?

Skewed to the left.

Symmetric

Skewed to the right.

(b) Two measures of center for this distribution are 1 friend and 5.3 friends. Which is most likely to be the mean and which is most likely to be the median?

Mean=

Median=

----------------------------------

a)

as proportion of people with 0 friends is 43% whcih is on left side and maximum ; and % decrease with increasing number of friends

skewed to the right

b)

as it is skewed to the right ; therefore mean is greater than median

mean=5.3

median=1

[since for skwewed to the right distribution :mean is always greater than median, therefore higher value should be mean which is 5.3 and lower value is median which is 1]

Part(a): Skewed to the right

Part(b) The required values are,

mean=5.3

median=1

a)

As a proportion of people with 0 friends are 43% which is on the left side and maximum; and % decrease with an increasing number of friends

skewed to the right

b)

As it is skewed to the right; therefore mean is greater than the median

mean=5.3

median=1

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A water cooler holds 15 liters of sports drink. Approximately how many gallons is this

Answers

The correct Anwser it is about 4 gallons because in 1 gallon tgere is 3.75 liters
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