Answer:
Step-by-step explanation:
(a)
The distribution of X is Normal Distribution with mean [tex]= \mu =17[/tex] and Variance [tex]= \sigma^{2} = 16 \ i.e., X \sim N (17, 16),[/tex]
(b)
The distribution of [tex]\bar{x}[/tex] is Normal Distribution with mean [tex]= \mu =17[/tex] and Variance = [tex]\sigma^{2}/n = 16/15= 1.0667[/tex].i.e., [tex]\bar{x}\sim N(17,1.0667)[/tex]
c)
To find P(15.5 < X < 18):
Case 1: For X from 15.5 to mid value:
Z = (15.5 - 17)/4 = - 0.375
Table of Area Under Standard Normal Curve gives area = 0.1480
Case 2: For X from mid value to 18:
Z = (18 - 17)/4 = 0.25
Table of Area Under Standard Normal Curve gives area = 0.0987
So,
P(15.5 < X< 18) = 0.1480 +0.0987 = 0.2467
So,
Answer is:
0.2467
(d)
[tex]SE = \sigma/\sqrt{n}\\\\= 4/\sqrt{15}[/tex]
= 1.0328
To find [tex]P(15.5 < \bar{x}< 18):[/tex]
Case 1: For [tex]\bar{x}[/tex] from 15.5 to mid value:
Z = (15.5 - 17)/1.0328 = - 1.4524
Table of Area Under Standard Normal Curve gives area = 0.4265
Case 2: For X from mid value to 18:
Z = (18 - 17)/1.0328 = 0.9682
Table of Area Under Standard Normal Curve gives area = 0.3340
So,
[tex]P(15.5 < \bar{x}< 18) = 0.4265 + 0.3340 = 0.7605[/tex]
So,
Answer is:
0.7605
(e)
Correct option:
No
because Population SD is provided.
(f)
(i)
Q1 is given by:
[tex]- 0.6745 = (\bar{x} - 17)/1.0328[/tex]
So,
X = 17 - (0.6745 * 1.0328) = 17 - 0.6966 = 16.3034
So,
Q1 = 16.3034
(ii)
Q3 is given by:
[tex]0.6745 = (\bar{x} - 17)/1.0328[/tex]
So,
X = 17 + (0.6745 * 1.0328) = 17 + 0.6966 = 17.6966
So,
Q3= 17.6966
(iii)
IQR = Q3 - Q1 = 17.6966 - 16.3034 = 1.3932
So
Answers are:
Q1 = 16.3034 ounces
Q3 = 17.6966 Ounces
IQR = 1.3932 Ounces
Please help me i need the answer if i knew it i will complete all of them by my self (: .
The right answer is 100 units^2
please see the attached picture for full solution
Hope it helps
Good luck on your assignment,
g Gravel is being dumped from a conveyor belt at a rate of 10 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 6 ft high
Answer:
0.3537 feet per minute.
Step-by-step explanation:
Gravel is being dumped from a conveyor belt at a rate of 10 ft3/min. Since we are told that the shape formed is a cone, the rate of change of the volume of the cone.
[tex]\dfrac{dV}{dt}=10$ ft^3/min[/tex]
[tex]\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h[/tex]
If the Base Diameter = Height of the Cone
The radius of the Cone = h/2
Therefore,
[tex]\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}[/tex]
[tex]\text{Rate of Change of the Volume}, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}[/tex]
Therefore: [tex]\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=10[/tex]
We want to determine how fast is the height of the pile is increasing when the pile is 6 feet high.
[tex]When h=6$ feet$\\\dfrac{3\pi *6^2}{12}\dfrac{dh}{dt}=10\\9\pi \dfrac{dh}{dt}=10\\ \dfrac{dh}{dt}= \dfrac{10}{9\pi}\\ \dfrac{dh}{dt}=0.3537$ feet per minute[/tex]
When the pile is 6 feet high, the height of the pile is increasing at a rate of 0.3537 feet per minute.
9. The mean is defined as the
A. number that shows up most often in a data set.
B. average of a data set.
C. middle of the data set.
D. range of the data set.
Answer:
B. Average of the data set
Step-by-step explanation:
The mean is defined as the average of a data set and it's formula is
Mean = [tex]\frac{sum of observations}{number of observations}[/tex]
Determine the number of ways three trumpet players out of 6 are chosen for 1st chair, 2nd chair, and 3rd chair.
Answer:
120 ways
Step-by-step explanation:
There are 3 spots and 6 options
_ _ _
1 2 3
6 ways for 1st chair to be chosen
5 ways for 2nd chair to be chosen (1st chair is chosen already, so there are 5 players left)
4 ways for 3rd chair to be chosen (1st and 2nd are already chosen, only 4 players left)
Multiply 6*5*4 to find the total number of ways (120)
Which cosine function has maximum of 0.5, a minimum of -0.5, and a period of 2(pi)/3
Answer:
The answer is "[tex]\bold{y=0.5 \cos 3 \theta}[/tex]"
Step-by-step explanation:
The choices were missing the question so the answer to this question can be defined as follows:
The answer is [tex]y= 0.5 \cos 3\theta[/tex] because:
[tex]\Rightarrow -1 \leq \cos 3 \theta \leq 1\\\\\Rightarrow -0.5 \leq \cos 3 \theta \leq 0.5\\[/tex]
So, the maximum value is = 0.5 and the minimum value is = -0.5 of [tex]\frac{2\pi}{3}[/tex].
Answer:
D. y= 0.5 cos 3 theta
Step-by-step explanation:
Please answer this correctly
Answer:
pic wont load
Step-by-step explanation:
Answer:
The quarter circle's area is 38.47 yard²
Step-by-step explanation:
The area of a full circle is pi * r ²
The area of a quarter circle is 1/4 * pi * r ²
Given:
Use 3.14 for pi
Round to the nearest hundredths.
Perimeter of quarter circle is 24.99 yards
For r you must leave it as 'r' because we do not know it for now...
1. Circumference of a full circle = 2* pi * r
2. 1/4 * ( 2 * pi * r )
1/4 * ( 2 * 3.14 * r )
1/2 * 3.14 * r
1.57 * r
3 Since r = 'r'
We have to 2 sides running from the centre of the 'pie' to the left and right of the quarter circle which both have a length of exactly 'r'. So you just add 2 * r.
4. The outcome of step 2 + step 3 is the perimeter of quarter circle, which was given as 24.99 inch
1.57 * r + 2 * r = 24.99
( 1.57 + 2 ) * r = 24.99
3.57 * r = 24.99
Divide left and right of the = sign by 3.57
3.57 / 3.57 * r = 24.99 / 3.57
1 * r = 24.99 / 3.57
r = 7
The area of a quarter circle is 1/4 * pi * r ²
1/4 * pi * 7²
1/4 * 49 * pi
49/4 * pi
49/4 * 3.14
38.465
Round to the nearest hundredths gives 38.47 yard²
The quarter circle's area is 38.47 yard²
please answer this correctly
Answer:
557
Step-by-step explanation:
l x w
13x24
13x7
22x7
557
Please answer this correctly
Answer:
Band: 30%
Chorus: 18%
Painting: 21%
Robotics: 14%
Coding: 17%
as a last-minute deal Don and Mary booked a 7 day cruise for a total of $670 if the normal price for a couple is $1340, what discount percent did Don and Mary recieve?
Answer:
Don and Mary received a discount of 50%.
Step-by-step explanation:
Initially, we use a rule of three to find the percentage of the initial price that they paid.
The discount is 100% subtracted by the percentage they paid.
Percentage they paid:
The normal price for a couple is $1340, which is 100%.
They paid $670, which is x%. We have to find x.
$1340 - 100%
$670 - x%
[tex]1340x = 100*670[/tex]
[tex]x = \frac{100*670}{1340}[/tex]
[tex]x = 50[/tex]
They paid 50% of the original price.
What discount percent did Don and Mary recieve?
100 - 50% = 50%
Don and Mary received a discount of 50%.
A swimming pool is to be drained. The pool is shaped like a Rectangular prism with length 12m , with 10 m, and depth 3m. Suppose water is pumped out of the pool at a rate of 18 m3 per hour.if the pool starts completely full , how many hours does it take to empty the pool ?
Answer:
20 hours
Step-by-step explanation:
first calculate volume:
12x10x3=360
then divide by 18
360/18=20
So 20 hours in total
Write down five numbers with a mode of 6.
Answer:
6 4 5 6 7
Step-by-step explanation:
The mode would be 5. The first 2 letters of MODE are MO, which can be an abbreviation for MOST OFTEN.
Which of the following represents "two times the sum of a number and fifteen is equal to six times the number?"
A. 2(6N + 15) = N
B. 2N + 15 = 6N
C. 2(N + 15) = 6N
Pls help me with this
Answer:
x = 1.5
Step-by-step explanation:
Given
[tex]\frac{x}{2} \geq 0.75[/tex]
[tex]\frac{x}{2} < 2.5[/tex]
Required
Find the value of x.
First, the inequalities need to be rewritten and merged;
if [tex]\frac{x}{2} \geq 0.75[/tex], then
[tex]0.75 \leq \frac{x}{2}[/tex]
Multiply both sides by 2
[tex]2 * 0.75 \leq \frac{x}{2} * 2[/tex]
[tex]1.5 \leq x[/tex]
Similarly;
[tex]\frac{x}{2} < 2.5[/tex]
Multiply both sides by 2
[tex]2 * \frac{x}{2} < 2.5 * 2[/tex]
[tex]x < 5[/tex]
Merging these results together; to give
[tex]1.5 \leq x < 5[/tex]
This means that the range of values of x is from 1.5 to 4.9999....
From the question, x is the smallest rational number; from the range above ([tex]1.5 \leq x < 5[/tex]), the minimum value of x is 1.5 and 1.5 is a rational number;
Hence, x = 1.5
Bonita said that the product of 5/6 x 1 2/3 is 7/3.
How can you tell that her answer is wrong.
Answer:
Bonita's product is too large
Step-by-step explanation:
The two factors in the problem are (5/6) and (5/3). The factor 5/6 is less than 1, ensuring that the product will be less than 5/3.
Bonita's result of 7/3 is more than 5/3, so is too large to be the product.
Please answer this correctly
Answer:
Area of the figure = 254.5 cm²
Step-by-step explanation:
Area of rectangle = Length × Width
Area of triangle = 1/2(base × Height)
Dividing the figure into parts for convenience
So,
Rectangle 1 (the uppermost):
4 × 6 = 24 cm²
Rectangle 2 (below rectangle 1):
15 × 8 = 120 cm²
Rectangle 3 (with rectangle 2):
11 × 4 = 44 cm²
Triangle 1 :
1/2(7 × 19) = 133/2 = 66.5 cm²
Now adding up all to get the area of the figure:
Area of the figure = 24 + 120 + 44 + 66.5
Area of the figure = 254.5 cm²
The percent, X , of shrinkage o n drying for a certain type of plastic clay has an average shrinkage percentage :, where parameter : is unknown. A random sample of 45 specimens from this clay showed an average shrinking percentage of 18.4 and a standard deviation of 2.2.
Required:
a. Estimate at 5% level of significance whether the true average shrinkage percentage U: is greater than 17.5 and write your conclusion.
b. Report the p-value.
Answer:
a) [tex]t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744[/tex]
The degrees of freedom are given by:
[tex]df=n-1=45-1=44[/tex]
The critical value for this case is [tex]t_{\alpha}=1.68[/tex] since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4
b) [tex]p_v =P(t_{(44)}>2.744)=0.0044[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=18.4[/tex] represent the sample mean
[tex]s=2.2[/tex] represent the sample standard deviation
[tex]n=45[/tex] sample size
[tex]\mu_o =17.5[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Part a
We want to test if the true mean is higher than 17.5, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 17.5[/tex]
Alternative hypothesis:[tex]\mu > 17.5[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing we got:
[tex]t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744[/tex]
The degrees of freedom are given by:
[tex]df=n-1=45-1=44[/tex]
The critical value for this case is [tex]t_{\alpha}=1.68[/tex] since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4
Part b
The p value would be given by:
[tex]p_v =P(t_{(44)}>2.744)=0.0044[/tex]
I need help with this one
Answer:
Top right
Step-by-step explanation:
The solution to a system of equation is where the two graphs cross
The top right lines cross at (5,-3)
2 number cubes are rolled
what is the probability that the first lands on an odd number and the second lands on an even number?
Answer:
1/4
Step-by-step explanation:
1/2 times 1/2
1/2 because there is 3 odds and 3 evens
the total is 6
3/6 equals to 1/2
so 1/2 times 1/2 is 1/4
??!!!?!?
.....
....
...
Answer:
A) (3,2)
Step-by-step explanation:
Conditions:
x+y ≤ 6x ≥ 0y ≥ 0A) (3,2)
yes, as all 3 conditions are met3+2≤6, 3≥0, 2≥0B) (0,7)
no, as the first condition is not met0+7 > 63. Which of the following values is not possible in probability?
A. P(x) = 1
B. x P(x) = 3 C. P(x) = 0.5
D. P(x) = -0.5
Answer:
D . P(x)=-0.5
Step-by-step explanation:
i think please mark my answer as a brainliest answer and follow me.
A shareholders' group, in lodging a protest, claimed that the mean tenure for a chief executive office (CEO) was at least eight years. A survey of companies reported in the Wall Street Journal found a sample mean tenure x = 7.56 of years for CEOs with a standard deviation of years s = 6.67 years.
A. Formulate hypotheses that can be used to challenge the validity of the claim made by the shareholders' group.
B. Assume 70 companies were included in the sample. What is the p-value for your hypothesis test?
C. At α = 0.02, what is your conclusion?
Answer:
could be c might be a also
Step-by-step explanation:
During the worst periods of inflation in America, the price of food increased at a rate of 12 % per month. If your food bill was $300 one month during this period, what was it two months later?
Exponential; $337.08
Linear; $672.00
Exponential; $376.32
Linear; $372.00
Answer:
Exponential; $376.32
Step-by-step explanation:
Generally, an increase of 12% in a month means the prices are 12% more than they were in the previous month. That is, the value has been multiplied by 1.12.
The same would be true for the second month, so the overall multiplier for the two months is ...
(1.12)(1.12) = 1.12^2 = 1.2544
This makes the food bill for the second month amount to ...
1.2544 × $300 = $376.32
_____
As with all percentages, you need to be clear about what base is being used. Here, we have assumed the base for a monthly increase is the value at the beginning of the month.
If, instead, it is the value at the beginning of the year, then the increase is linear, not exponential. 12% of the value at the beginning of the year is the same throughout the year.
Find the area of a regular hexagon with a side length of 5cm, Round to the nearest tenth.
Answer:
i think its 64.95cm
Step-by-step explanation:
Five people (Aaron , Byron , Carina , Duncan , and Evelyn ) form a club, Nequals {A, B, C, D, E}. Carina and Evelyn are women, and the others are men. If they choose a treasurer randomly, find the odds in favor of Evelyn becoming treasurer . The odds in favor of Evelyn becoming treasurer are
================================================
Explanation:
When we talk about "odds in favor", we will use a colon to separate two whole numbers. The first number represents the number of ways for Evelyn to be chosen treasurer (just one way) and the second number represents all the ways she doesn't get chosen (the four other people)
Put another way, writing "odds in favor are 1:4" basically means "there's 1 way to get Evelyn elected and 4 ways for her to not get elected"
Instead of writing 1:4 you could write "1 to 4"
-----------
Side note: Contrast this with "odds against" and the ratio would flip from 1:4 to 4:1. Same idea, but the number of failures is listed first because we're focusing on the "against" (instead of "favor") portion. We read "4:1" as "4 to 1".
The odds in favor of Evelyn becoming treasurer are 1:5 or 1/5.
To determine the odds in favor of Evelyn becoming treasurer, we need to know the total number of possible outcomes and the number of favorable outcomes.
There are five members in the club, so there are five possible outcomes for the treasurer position, one for each member. Since Evelyn is one of the five members, she has one favorable outcome.
Therefore, the odds in favor of Evelyn becoming treasurer are 1:5 or 1/5.
Learn more about odds in favor here:
https://brainly.com/question/32587212
#SPJ4
A supermarket is redesigning it’s checkout lanes. Design A has a sample size of 50, sample mean of 4.1 minutes, and sample standard deviation of 2.2 minutes. Design B has a sample size of 50, sample mean of 3.5 minutes, and sample standard deviation of 1.5 minutes. At the 0.05 level of significance, determine if their is evidence that the checkout times of the two systems differ.
Answer:
The calculated value t = 1.57736 < 1.9845 at 5 % level of significance
Null hypothesis is accepted at 5 % level of significance
There is no significance difference between Design A and Design B
Step-by-step explanation:
Given sample size of design A
n₁ = 50
sample mean of design A x⁻₁ = 4.1 minutes
Sample standard deviation S₁ = 2.2 minutes
Given sample size of design B
n₂ = 50
sample mean of design A x⁻₂ = 3.5 minutes
Sample standard deviation S₂ = 1.5 minutes
Null Hypothesis : H₀ : There is no significance difference between Design A and Design B
Alternative Hypothesis : H₁:There is significance difference between Design A and Design B
Level of significance ∝ = 0.05
Test statistic
[tex]t = \frac{x^{-} _{1}- x^{-} _{2} }{\sqrt{S^{2} (\frac{1}{n_{1} }+\frac{1}{n_{2} }) } }[/tex]
where
[tex]S^{2} = \frac{n_{1} S_{1} ^{2} +n_{2} S^2_{2} }{n_{1} +n_{2} -2}[/tex]
[tex]S^{2} = \frac{50 (2.2)^{2} +50(1.5)^2}{50+50-2}[/tex]
On calculation , we get
S² = 3.6173
Test statistic
[tex]t = \frac{4.1-3.5}{\sqrt{3.617(\frac{1}{50} +\frac{1}{50} }) }[/tex]
On calculation , we get
t = 1.57736
Degrees of freedom
ν = n₁ + n₂ -2 = 50 +50 -2 =98
t₀.₀₂₅ ,₉₈ = 1.9845
The calculated value t = 1.57736 < 1.9845 at 5 % level of significance
null hypothesis is accepted
A tank contains 180 liters of fluid in which 50 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 6 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.
Answer:
[tex]\mathbf{A(t) = 180 - 130e ^{-\dfrac{t}{30}}}[/tex]
Step-by-step explanation:
Given that:
A tank contains 180 liters of fluid in which 50 grams dissolved inside.
Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 6 L/min
The salt pumped out[tex]= \dfrac{6 L}{180 L} = \dfrac{1}{30}[/tex] of initial amount added salt
At (t = 0) = 50
To determine the number A (t)
[tex]\dfrac{dA}{dt}=Rate_{in} - Rate _{out}[/tex]
[tex]A' = 6 - \dfrac{1}{30}A[/tex]
[tex]A' + \dfrac{1}{30}A = 6[/tex]
Integrating factor [tex]y = e^{\int\limits pdt[/tex]
[tex]y = e^{\int\limits \dfrac{1}{30}dt}[/tex]
[tex]y = e^{\dfrac{t}{30}}[/tex]
[tex](e^{ \frac{t}{30}}A)' =4 e ^{\dfrac{t}{30}}+c[/tex]
Taking integral on the both sides;
[tex]Ae ^{\dfrac{t}{30}}= 6 * 30 e^{\dfrac{t}{30}} + c[/tex]
[tex]A = 180+ ce^ {-\dfrac{t}{30}}[/tex]
At A(t = 0) = 50
50 = 180 + C (assuming C = [tex]ce ^{-\dfrac{t}{30}}[/tex])
C = 50 - 180
C = 130
[tex]\mathbf{A(t) = 180 - 130e ^{-\dfrac{t}{30}}}[/tex]
write the equation of the line that is parallel to 2x-y=15 and passes through the point (3,7)
Answer:
work is shown and pictured
Erin has previously recorded all credit card activity manually using the Expense transaction screen and reconciled the account using the Reconciliation Tool. After connecting her credit card in the Banking Center, she doesn’t see any matches for the transactions she previously entered and reconciled.
Answer:
The steps Erin has to take for the reconciliation of her account and activities is as follows: Select the reconciled transactions, Select Batch actions, and Modify the selected ones.
Step-by-step explanation:
Solution
Since Erin could not detect any matches for the transactions she has entered before and enrolled, she needs to take the following processes to reconcile back all her credit activities which is stated below:
Process 1 :Select the reconciled transactions
Process 2 :Batch Actions
Process 3: Modify Selected
From the process stated above Erin can first of all choose the reconciled transactions, after that she can select the batch actions and lastly modify the ones that was selected with the aim of putting or adding them back in the account reconciliation.
Listed below are head injury measurements from small cars that were tested in crashes. The measurements are in "hic," which is a measurement of a standard "head injury criterion," (lower "hic" values correspond to safer cars). The listed values correspond to cars A, B, C, D, E, F, and G, respectively. Find the
a. mean,
b. median,
c. midrange,
d. mode for the data.
Also complete parts e. and f. 514 541 302 400 507 406 369
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Listed below are head injury measurements from small cars that were tested in crashes. The measurements are in "hic," which is a measurement of a standard "head injury criterion," (lower "hic" values correspond to safer cars). The listed values correspond to cars A, B, C, D, E, F, and G, respectively.
514 541 302 400 507 406 369
Find the
a. mean,
b. median,
c. midrange,
d. mode for the data.
Also complete parts e. and f.
e. Which car appears to be the safest?
f. Based on these limited results, do small cars appear to have about the same risk of head injury in a crash?
Answer:
a) Mean = 434.14
b) Median = 406
c) Midrange = 421.5
d) Mode = 0
e) Car C appears to be the safest
f) The small cars does not appear to have about the same risk of head injury in a crash.
Step-by-step explanation:
We are given the head injury measurements from small cars that were tested in crashes.
The measurements are in "hic," which is a measurement of a standard "head injury criterion.
The listed values are;
A = 514
B = 541
C = 302
D = 400
E = 507
F = 406
G = 369
a) Mean
The mean of the measurements is given by
Mean = Sum of measurements/ Number of measurements
Mean = (514 + 541 + 302 + 400 + 507 + 406 + 369)/7
Mean = 3039/7
Mean = 434.14
b) Median
Arrange the measurements in ascending order (low to high)
302, 369, 400, 406, 507, 514, 541
The median is given by
Median = (n + 1)/2
Median = (7 + 1)/2
Median = 8/2
Median = 4th
Therefore, the 4th measurement is the median that is 406
Median = 406
c) Mid-range
The midrange is given by
Midrange = (Max + Min)/2
The maximum measurement in the data set is 541
The minimum measurement in the data set is 302
Midrange = (541 + 302)/2
Midrange = 843/2
Midrange = 421.5
d) Mode for the data
The mode of the data set is the most repeated measurement.
302, 369, 400, 406, 507, 514, 541
In the given data set we don't have any repeated measurement therefore, there is no mode or we can say the mode of this data set is 0.
Mode = 0
e) Which car appears to be the safest?
Since we are given that the measurements are in "hic," which is a measurement of a standard "head injury criterion," (lower "hic" values correspond to safer cars)
The lowest hic value corresponds to car C that is 302
Therefore, car C appears to be the safest among other cars.
f) Based on these limited results, do small cars appear to have about the same risk of head injury in a crash?
302, 369, 400, 406, 507, 514, 541
As you can notice, the hic values differ a lot from each other therefore, we can conclude that the small cars does not appear to have about the same risk of head injury in a crash.
A physicist examines 25 water samples for nitrate concentration. The mean nitrate concentration for the sample data is 0.165 cc/cubic meter with a standard deviation of 0.0783. Determine the 80% confidence interval for the population mean nitrate concentration. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
The 80% confidence interval for the the population mean nitrate concentration is (0.144, 0.186).
Critical value t=1.318
Step-by-step explanation:
We have to calculate a 80% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=0.165.
The sample size is N=25.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{0.078}{\sqrt{25}}=\dfrac{0.078}{5}=0.016[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=25-1=24[/tex]
The t-value for a 80% confidence interval and 24 degrees of freedom is t=1.318.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=1.318 \cdot 0.016=0.021[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 0.165-0.021=0.144\\\\UL=M+t \cdot s_M = 0.165+0.021=0.186[/tex]
The 80% confidence interval for the population mean nitrate concentration is (0.144, 0.186).