Answer:
The sample proportion for the births that are girls is 0.505. It is slightly higher than the expected value of 0.5, but the right way to answer if it is an unusual proportion is by performing an hypothesis test.
The hypothesis test results in not enough evidence to claim that the outcome is unlikely. This sample result has a probability of 0.7627 of appearing by pure chance in a population with proportion p=0.5.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the proportion of girls birth differs significantly from the expected proportion (50%).
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.5\\\\H_a:\pi\neq 0.5[/tex]
The significance level is 0.05.
The sample has a size n=1100.
The sample proportion is p=0.505.
p=X/n=556/1100=0.505
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{1100}}\\\\\\ \sigma_p=\sqrt{0.000227}=0.015[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.505-0.5-0.5/1100}{0.015}=\dfrac{0.005}{0.015}=0.302[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=2\cdot P(z>0.302)=0.7627[/tex]
As the P-value (0.7627) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the proportion of girls birth differs significantly from the expected proportion (50%).
The first few steps in solving the quadratic equation 9x2 + 49x = 22 − 5x by completing the square are shown. 9x2 + 49x = 22 − 5x 9x2 + 54x = 22 9(x2 + 6x) = 22 Which is the best step to do next to solve the equation by completing the square? 9(x2 + 6x + 3) = 25 9(x2 + 6x + 3) = 49 9(x2 + 6x + 9) = 31 9(x2 + 6x + 9) = 103
Answer:
The Answer is : 9(x2 + 6x + 9) = 103
Step-by-step explanation:
Option D on edge2020 i got a 100 on the quiz
The resulting quadratic equation is [tex](x+3)^2-103/9=0[/tex]
Quadratic equationGiven the quadratic equation [tex]9x^2 + 49x = 22 - 5x[/tex]
Write in standard form:
[tex]9x^2 + 49x = 22 - 5x\\ 9x^2 + 49x + 5x -22= 0\\ 9x^2+54x-22=0[/tex]
Divide through by 9
[tex]x^2+6x-22/9=0\\ [/tex]
complete the square to have:
[tex]x^2+6x-22/9+3^2-3^2=0\\ x^2+6x+3^2-9-22/9 = 0\\ (x+3)^2-103/9=0[/tex]
Hence the resulting quadratic equation is [tex](x+3)^2-103/9=0[/tex]
Learn more on completing the square here: https://brainly.com/question/1596209
The length of a rectangle is 4 inches longer than the width. If the area is 390 square inches, find the rectangle's dimensions. Round your answers to the nearest tenth of an inch.
Answer:
17.8 in x 21.8 in
Step-by-step explanation:
Given w=width and l=length
w*l=390
l=w+4, therefore w*(w+4)=390
w^2+4w=390
w^2+4w-390=0
Quadratic equation, solve as such
w=-21.8 or 17.8
Solution can't be negative so w=17.8 in
l=w+4 so l=21.8
What is the probability that a senior Physics major and then a sophomore Physics major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places
Answer:
The probability that a senior Physics major and then a sophomore Physics major are chosen at random is 0.0095.
Step-by-step explanation:
The complete question is:
There are 103 students in a physics class. The instructor must choose two students at random.
Students in a Physics Class
Academic Year Physics majors Non-Physics majors
Freshmen 17 15
Sophomores 20 14
Juniors 11 17
Seniors 5 4
What is the probability that a senior Physics major and then a sophomore Physics major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places.
Solution:
There are a total of N = 103 students present in a Physics class.
Some of the students are Physics Major and some are not.
The instructor has to select two students at random.
The instructor first selects a senior Physics major and then a sophomore Physics major.
Compute the probability of selecting a senior Physics major student as follows:
[tex]P(\text{Senior Physics Major})=\frac{n(\text{Senior Physics Major}) }{N}[/tex]
[tex]=\frac{5}{103}\\\\=0.04854369\\\\\approx 0.0485[/tex]
Now he two students are selected without replacement.
So, after selecting a senior Physics major student there are 102 students remaining in the class.
Compute the probability of selecting a sophomore Physics major student as follows:
[tex]P(\text{Sophomore Physics Major})=\frac{n(\text{Sophomore Physics Major}) }{N}[/tex]
[tex]=\frac{20}{102}\\\\=0.1960784314\\\\\approx 0.1961[/tex]
Compute the probability that a senior Physics major and then a sophomore Physics major are chosen at random as follows:
[tex]P(\text{Senior}\cap \text{Sophomore})=P(\text{Senior})\times P(\text{Sophomore})[/tex]
[tex]=0.0485\times 0.1961\\\\=0.00951085\\\\\approx 0.0095[/tex]
Thus, the probability that a senior Physics major and then a sophomore Physics major are chosen at random is 0.0095.
2 Points
Which is a kingdom?
O A. Prokarya
B. Protista
C. Mammalia
O D. Chordata
Answer:
Protista
Step-by-step explanation:
Archaebacteria.
Eubacteria.
Protista.
Fungi.
Plantae.
Animalia.
These are the 6 kingdoms
What is the result of adding these two equations? 2x+3y=-5 5x-y=-12
Answer:
[tex]x = \frac{-41}{17} , y = \frac{-1}{17}[/tex]
Step-by-step explanation:
Step(i):-
Given equations are 2 x+3 y=-5 ...(i)
5 x-y=-12 ...(ii)
Multiply equation (ii) by '3'
2 x + 3 y = -5
15 x - 3 y = - 36
17 x = - 41
[tex]x = \frac{-41}{17}[/tex]
Step(ii):-
Substitute [tex]x = \frac{-41}{17}[/tex] in equation (i)
2 ([tex]\frac{-41}{17}[/tex]+3 y=-5
3 y = - 5 + [tex]\frac{82}{17}[/tex]
[tex]3 y = \frac{-85 + 82}{17} = \frac{-3}{17}[/tex]
[tex]y = \frac{-1}{17}[/tex]
The solution of the two equations
( x, y ) = [tex](\frac{-41}{17} , \frac{-1}{17})[/tex]
If 4000 hours= 240,000 minutes and you make a 10 minute video, how many people will need to view the video to get 4000 hours of view time?
Answer:
24000
Step-by-step explanation:
because 24000 * 10 =240000
What is the simplified value of the exponential expression 27 1/3?
1/3
1/9
3
9
Answer:3
Step-by-step explanation:
Answer:
C.3
Step-by-step explanation:
What is the purchase price of the land
Answer:
Answer:B. $100,000
Step-by-step explanation:
x is the number of years since the purchase of the land.
That means that when 0 years have passed by, it is when the land was purchased.
At x = 0, the price of the land was $100,000.
That means that the purchase price of the land is $100,000.
What’s the correct answer for this question?
Answer:
C.
Step-by-step explanation:
First finding height using Pythagoras theorem
(H)²=(B)²+(P)²
8.2²=5.4²+P²
P² = 67.24 - 29.16
P² = 38.08
P = 6.2
Now
Volume of cone = (1/3)πr²h
= (1/3)(3.14)(5.4)²(6.2)
= (1/3)(567.9)
= 189.2 cm³
Consider the polynomial 9x2 – 16.
Answer: 2
Step-by-step explanation:
9 × 2 - 16
18 - 16
2
A computer manufacturer conducted a survey. It showed that a younger customer will not necessarily purchase a lower or higher priced computer. What is likely true? There is no correlation between age and purchase price. There is a correlation between age and purchase price. There may or may not be causation. Further studies would have to be done to determine this. There is a correlation between age and purchase price. There is probably also causation. This is because there is likely a decrease in the purchase price with a decrease in age.
Answer:
There is no correlation between age and purchase price
Step-by-step explanation:
In the survey, the researcher found out that a younger customer will not necessarily purchase a lower or higher priced computer thing it is likely true that there might be no correlation between purchase price and age.
It assumes that a younger customer can buy either buy a lower priced computer or can also buy a higher priced if he or she has the money for it.
Every product manufactured by a company goes through 6 different tests before being shipped out. It is known that the probability that a product passes any single test is 0.9 and the tests are independent. Only those products that pass the first three tests and also pass at least one of the three remaining tests are shipped out. Find the probability that a manufactured product is shipped out.
Answer:
The Probability that the product is shipped out is 0.7283
Step-by-step explanation:
Here, we are given that, a product passes through 6 tests before it is shipped out and a product is shipped out only if it passes all the first 3 tests and at least 1 of the remaining 3 tests.
We have P(pass)= 0.9, is the Probability of passing any test.
Which implies, P(fail)= 1- 0.9= 0.1
We have to find the Probability that the product is shipped out.
P(product is shipped out) = P(it passes first 3 tests )*P(passes at least 1 of the remaining 3 tests) •••••••••••(i)
We can take the product as the tests are Independent.
Now, let us obtain
P(it passes first 3 tests ) = P(pass)*P(pass)*P(pass)
=P(pass)]^3 = (0.9)^3 = 0.729
Hence, P( it passes first 3 tests)= 0.729 •••••••(ii)
Now,
P(passes at least 1 of the remaining 3 tests)
= 1-P(fails all the 3 remaining tests)
= 1-(0.1)^3 = 1 - 0.001 = 0.999
Hence,
P(passes atleast 1 of the remaining 3 tests)=0.999 ••••••••(iii)
Now, substituting the 2nd and 3rd equations in the first equation, we have;
P(product is shipped out) = P(it passes first 3 tests )*P(passes at least 1 of the remaining 3 tests)
= (0.729)*(0.999)
= 0.728271
= 0.7283
If f(x) = –8 – 5x, what is f(–4)?
Answer:
12
Step-by-step explanation:
f(-4) = -8-5(-4) = -8+20 = 12
Answer:
f(-4) = 12
Step-by-step explanation:
f(-4) = -8 - 5(-4)
= -8 + 20
= 12
A mattress store sells only king, queen and twin-size mattresses. Sales records at the store indicate that the number of queen-size mattresses sold is one-fourth the number of king and twin-size mattresses combined. Records also indicate that three times as many king-size mattresses are sold as twin-size mattresses. Calculate the probability that the next mattress sold is either king or queen-size.
Answer:
The probability that the next mattress sold is either king or queen-size is P=0.8.
Step-by-step explanation:
We have 3 types of matress: queen size (Q), king size (K) and twin size (T).
We will treat the probability as the proportion (or relative frequency) of sales of each type of matress.
We know that the number of queen-size mattresses sold is one-fourth the number of king and twin-size mattresses combined. This can be expressed as:
[tex]P_Q=\dfrac{P_K+P_T}{4}\\\\\\4P_Q-P_K-P_T=0[/tex]
We also know that three times as many king-size mattresses are sold as twin-size mattresses. We can express that as:
[tex]P_K=3P_T\\\\P_K-3P_T=0[/tex]
Finally, we know that the sum of probablities has to be 1, or 100%.
[tex]P_Q+P_K+P_T=1[/tex]
We can solve this by sustitution:
[tex]P_K=3P_T\\\\4P_Q=P_K+P_T=3P_T+P_T=4P_T\\\\P_Q=P_T\\\\\\P_Q+P_K+P_T=1\\\\P_T+3P_T+P_T=1\\\\5P_T=1\\\\P_T=0.2\\\\\\P_Q=P_T=0.2\\\\P_K=3P_T=3\cdot0.2=0.6[/tex]
Now we know the probabilities of each of the matress types.
The probability that the next matress sold is either king or queen-size is:
[tex]P_K+P_Q=0.6+0.2=0.8[/tex]
I need help please help me is it 30?
Answer:
i think is 30$
Step-by-step explanation:
Answer:
B. $15.00
Step-by-step explanation:
Think about it this way:
3 = 1.50
6 = 3.00
8 = 4.00
12 = 6.00
If you divide each of the first numbers by the second, you'll get 2.
This means that every doughnut costs $0.50.
From there you just multiply .5 by 30
30
x .5
15
30 Donuts would cost 15 dollars.
Ok so the above is a little bit more of a complicated way to do it, but it'll be more efficient for a similar, but more difficult problem. The general goal of these problems is to find out what 1 of the item would cost. In this case it's $0.50, but you need to find that out in all of these problems.
brainliest is appreciated.
HELP! the function f(x)=200/x+10 models the cost per student of a field trip when x students go on the trip. how is the parent function f(x)=1/x transformed to create the function f(x)=200/x+10
Answer:
stretch of 200 shift up 10 units
Step-by-step explanation:
f(x)=1/x to 200/x+10
Multiply by 200 means a stretch of 200
f(x) = 200/x
Now shift up 10 units
f(x) = 200/x + 10
Answer:
It moves up 10 units
Step-by-step explanation:
f(x) =1/x to 200/x + 10
= 200/x
If we shift up 10 units, we get:
f(x) = 200/x + 10
Hope this helps!
find the slope of a line parallel to y=(2/5)x + (4/5)
Answer:
So if a line was parallel it would have same slope. You can search up what slope-intercept form means. But if you have an equation like this:
y = mx+b
The slope will be m. Your question is written in the form. 2/5 = m.
The slope is 2/5
The y-intercept is 4/5
Answer:
m=2/5
Step-by-step explanation:
Lines that are parallel have the exact same slope.
We have an equation in point slope form.
y=mx+b
where m is the slope and b is the y-intercept.
The slope is the number being multiplied by x. In the equation
y=2/5x+4/5
2/5 and x are being multiplied. Therefore, 2/5 is the slope. A line that is parallel will have the same slope of 2/5.
Which expressions are equivalent to 64^1Check all that apply
The right answers are:
4^38^22^6Hope it helps.
please see the attached picture for full solution
Good luck on your assignment
Find an Equation of a line with the given slope that passes through the point. Write the equation in the form Ax + By=C
M=3/2, (7,-2) -problem
Bridge math sails
Module 4B2
Answer:
c = 24 can i get brainliest
Step-by-step explanation:
Solve the equation and state a reason for each step.
23+11a-2c=12-2c
Simplifying
23 + 11a + -2c = 12 + -2c
Add '2c' to each side of the equation.
23 + 11a + -2c + 2c = 12 + -2c + 2c
Combine like terms: -2c + 2c = 0
23 + 11a + 0 = 12 + -2c + 2c
23 + 11a = 12 + -2c + 2c
Combine like terms: -2c + 2c = 0
23 + 11a = 12 + 0
23 + 11a = 12
Solving
23 + 11a = 12
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-23' to each side of the equation.
23 + -23 + 11a = 12 + -23
Combine like terms: 23 + -23 = 0
0 + 11a = 12 + -23
11a = 12 + -23
Combine like terms: 12 + -23 = -11
11a = -11
Divide each side by '11'.
a = -1
Simplifying
a = -1
A coffe storage bin contains 1500 grams of coffe beans. To make a cup of coffee, n grams of coffe beans are removed
Answer:
The amount remaining in coffee storage bin after making 10cups if coffee = (1500-10n) grams
Step-by-step explanation:
This question is incomplete as we are not told what to determine.
Let's consider the following question:
A coffee storage bin contains 1500 grams of coffee beans. To make a cup of coffee, n grams of coffee beans are removed. How many grams of coffee would be left after making 10 cups of coffee?
Solution:
Total amount of coffee in storage bin = 1500grams
To make one cup of coffee, we need n grams of coffee
The amount remaining for one cup = 1500grams - n grams
To make 10 cups of coffee, we would need = 10× n grams of coffee= 10n grams
The amount remaining in coffee storage bin after making 10cups of coffee = total amount in storage - amount for making 10cups
(1500-10n) grams
You are conducting a study to see if the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.3. A random sample of 735 men over the age of 50 found that 203 have their prostate regularly examined. Do the sample data provide convincing evidence to support the claim
Answer:
[tex]z=\frac{0.276 -0.3}{\sqrt{\frac{0.3(1-0.3)}{735}}}=-1.42[/tex]
Now we can claculate the p value with this formula:
[tex]p_v =P(z<-1.42)=0.0778[/tex]
If we use a signifiacn level of 5% we see that the p value is higher than 0.05 so then we have enough evidence to fail to reject the null hypothesis and we can't conclude that the true proportion is significantly higher than 0.3 at 5% of significance.
Step-by-step explanation:
Information to given
n=735 represent the random sample taken
X=203 represent the number of people who have their prostate regularly examined
[tex]\hat p=\frac{203}{735}=0.276[/tex] estimated proportion of people who have their prostate regularly examined
[tex]p_o=0.3[/tex] is the value to verify
z would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to test if the true proportion is less than 0.3, the ystem of hypothesis are.:
Null hypothesis:[tex]p \geq 0.3[/tex]
Alternative hypothesis:[tex]p < 0.3[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info we got:
[tex]z=\frac{0.276 -0.3}{\sqrt{\frac{0.3(1-0.3)}{735}}}=-1.42[/tex]
Now we can claculate the p value with this formula:
[tex]p_v =P(z<-1.42)=0.0778[/tex]
If we use a signifiacn level of 5% we see that the p value is higher than 0.05 so then we have enough evidence to fail to reject the null hypothesis and we can't conclude that the true proportion is significantly higher than 0.3 at 5% of significance.
Simplify.
(8^3)7 = 8n
Answer:
448I think
Step-by-step explanation:
Answer:21
Step-by-step explanation:
The probability of obtaining a defective 10-year old widget is 66.6%. For our purposes, the random variable will be the number of items that must be tested before finding the first defective 10-year old widget. Thus, this procedure yields a geometric distribution. Use some form of technology like Excel or StatDisk to find the probability distribution. (Report answers accurate to 4 decimal places.) k P(X = k) 1 .666 Correct 2 3 4 5 6 or greater
Answer:
For k = 1:
=NEGBINOMDIST(0, 1, 0.666) = 0.6660
For k = 2:
=NEGBINOMDIST(1, 1, 0.666) = 0.2224
For k = 3:
=NEGBINOMDIST(2, 1, 0.666) = 0.0743
For k = 4:
=NEGBINOMDIST(3, 1, 0.666) = 0.0248
For k = 5:
=NEGBINOMDIST(4, 1, 0.666) = 0.0083
For k = 6:
=NEGBINOMDIST(5, 1, 0.666) = 0.0028
Step-by-step explanation:
The probability of obtaining a defective 10-year old widget is 66.6%
p = 66.6% = 0.666
The probability of obtaining a non-defective 10-year old widget is
q = 1 - 0.666 = 0.334
The random variable will be the number of items that must be tested before finding the first defective 10-year old widget.
The geometric distribution is given by
[tex]$P(X = k) = p \times q^{k - 1}$[/tex]
Solving manually:
For k = 1:
[tex]P(X = 1) = 0.666 \times 0.334^{1 - 1} = 0.666 \times 0.334^{0} = 0.666[/tex]
For k = 2:
[tex]P(X = 2) = 0.666 \times 0.334^{2 - 1} = 0.666 \times 0.334^{1} = 0.2224[/tex]
For k = 3:
[tex]P(X = 3) = 0.666 \times 0.334^{3 - 1} = 0.666 \times 0.334^{2} = 0.0743[/tex]
For k = 4:
[tex]P(X = 4) = 0.666 \times 0.334^{4 - 1} = 0.666 \times 0.334^{3} = 0.0248[/tex]
For k = 5:
[tex]P(X = 5) = 0.666 \times 0.334^{5 - 1} = 0.666 \times 0.334^{4} = 0.0083[/tex]
For k = 6:
[tex]P(X = 6) = 0.666 \times 0.334^{6 - 1} = 0.666 \times 0.334^{5} = 0.0028[/tex]
Using Excel function:
NEGBINOMDIST(number_f, number_s, probability_s)
Where
number_f = k - 1 failures
number_s = no. of successes
probability_s = the probability of success
For the geometric distribution, let number_s = 1
For k = 1:
=NEGBINOMDIST(0, 1, 0.666) = 0.6660
For k = 2:
=NEGBINOMDIST(1, 1, 0.666) = 0.2224
For k = 3:
=NEGBINOMDIST(2, 1, 0.666) = 0.0743
For k = 4:
=NEGBINOMDIST(3, 1, 0.666) = 0.0248
For k = 5:
=NEGBINOMDIST(4, 1, 0.666) = 0.0083
For k = 6:
=NEGBINOMDIST(5, 1, 0.666) = 0.0028
As you can notice solving manually and using Excel yields the same results.
What’s the correct answer for this?
Answer:
C.
Step-by-step explanation:
According to theorem, congruent angles has congruent sides opposite to them so,
RS = TU
Now
12x+4 = 11x+15
12x-11x = 15-4
So
x = 11
Now
TU = 11x+15
= 11(11)+15
= 121+15
= 136 units
How many tons is 22,000 pounds?
Answer:
1 ton = 2,000 pounds
Step-by-step explanation:
With that said, 22,000 pounds is 11 tons because 2,000 x 11 = 22,000.
So 22,000 pounds is 11 tons.
Hope it helps and pls mark me brainliest if it did! :)
Q‒4. Suppose A is the set composed of all ordered pairs of positive integers. Let R be the relation defined on A where (a,b)R(c,d) means that a+d=b+c.
Prove that R is an equivalence relation.
Find [(2,4)].
Answer:
Step-by-step explanation:
REcall that given a set A, * is a equivalence relation over A if
- for a in A, then a*a.
- for a,b in A. If a*b, then b*a.
- for a,b,c in A. If a*b and b*c then a*c.
Consider A the set of all ordered pairs of positive integers.
- Let (a,b) in A. Then a+b = a+b. So, by definition (a,b)R(a,b).
- Let (a,b), (c,d) in A and suppose that (a,b)R(c,d) . Then, by definition a+d = b+c. Since the + is commutative over the integers, this implies that d+a = c+b. Then (c,d)R(a,b).
- Let (a,b),(c,d), (e,f) in A and suppose that (a,b)R(c,d) and (c,d)R(e,f). Then
a+d = b+c, c+f = d+e. We have that f = d+e-c. So a+f = a+d+e-c. From the first equation we find that a+d-c = b. Then a+f = b+e. So, by definition (a,b)R(e,f).
So R is an equivalence relation.
[(a,b)] is the equivalence class of (a,b). This is by definition, finding all the elements of A that are equivalente to (a,b).
Let us find all the possible elements of A that are equivalent to (2,4). Let (a,b)R(2,4) Then a+4 = b+2. This implies that a+2 = b. So all the elements of the form (a,a+2) are part of this class.
A newborn baby whose Apgar score is over 6 is classified as normal and this happens in 80% of births. As a quality control check, an auditor examined the records of 100 births. He would be suspicious if the number of normal births in the sample of 100 births fell below the lower limit of "usual." What is that lower limit?
Answer:
The lower limit is 72.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
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.
If X is more than 2 standard deviations from the mean, it is unusual.
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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question, we have that:
[tex]n = 100, p = 0.8[/tex]
So
[tex]\mu = 0.8, s = \sqrt{\frac{0.8*0.2}{100}} = 0.04[/tex]
He would be suspicious if the number of normal births in the sample of 100 births fell below the lower limit of "usual." What is that lower limit?
2 standard deviations below the mean is the lower limit, so X when Z = -2.
Proportion:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-2 = \frac{X - 0.8}{0.04}[/tex]
[tex]X - 0.8 = -2*0.04[/tex]
[tex]X = 0.72[/tex]
Out of 100:
0.72*100 = 72
The lower limit is 72.
2x2 + 3x ANSWER TO THIS
Answer:
x(2x+3)
Step-by-step explanation:
Im guessing 2x2 is 2x^2
2x^2 + 3x = 0
x(2x+3)
Records on a fleet of trucks reveal that the average life of a set of spark plugs is normally distributed with a mean of 22,100 miles. The fleet owner purchased 18 sets and found that the sample average life was 23,400 miles; the sample standard deviation was 1,412 miles.
a) To decide if the sample data support the company records that the spark plugs average 22,100 miles, state your decision in terms of the null hypothesis. Use a 0.05 level of significance.
b) What is the critical value for the test using a 0.05 level of significance?
c) What is the test statistic?
d) What is your decision?
Answer:
a) We want to conduct a hypothesis in order to see if the true mean is 22100 or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 22100[/tex]
Alternative hypothesis:[tex]\mu \neq 22100[/tex]
b) We need to find the degrees of freedom given by:
[tex] df =n-1 = 18-1=17[/tex]
And the critical values for this case are:
[tex] t_{\alpha/2}= 2.110[/tex]
c) [tex]t=\frac{23400-22100}{\frac{1412}{\sqrt{18}}}=3.906[/tex]
d) Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 221100 mi
Step-by-step explanation:
Information provided
[tex]\bar X=23400[/tex] represent the sample mean
[tex]s=1412[/tex] represent the sample standard deviation
[tex]n=18[/tex] sample size
[tex]\mu_o =22100[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value
Part a
We want to conduct a hypothesis in order to see if the true mean is 22100 or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 22100[/tex]
Alternative hypothesis:[tex]\mu \neq 22100[/tex]
Part b
We need to find the degrees of freedom given by:
[tex] df =n-1 = 18-1=17[/tex]
And the critical values for this case are:
[tex] t_{\alpha/2}= 2.110[/tex]
Part c
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]t=\frac{23400-22100}{\frac{1412}{\sqrt{18}}}=3.906[/tex]
Part d
Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 221100 mi