he amount of pressure created from a air compressor spray is normally distributed with a mean of 10,000 pounds per square inch (PSI) and standard deviation of 800 PSI.

(1) For a random sample of n=4 sprays, what is the probability that the sample mean will be at least 10,200 PSI?
(2) For a random sample of n=4 sprays, what is the probability that the sample mean will be less than 9,900 PSI?

For a population of five individuals, bike ownership is as follows:
(A) = 2; (B) = 1; (C) = 3; (D) = 4; (E) = 2
Determine the probability distribution for the discrete random variable, x = # bikes:
(1) Calculate the population mean.
(2) Calculate the population standard deviation.
(3) For a sample size n=2, determine the mean number of bikes for the two person pair.
(4) How many two person outcomes lead to a mean of 1.5 (note: for consistency, count (A,B) and (B,A) as two separate outcomes)?
(5) What is the P(x̅) = 1.5?
(6) What is the mean of this sampling distribution (n=2)?
(7) What is the standard deviation of this sampling distribution (n=2)?

In 2017, a study on the salary distribution of Paris residents was conducted. Assume that the salaries were normally distributed.

A random sample of 10 salaries was selected and the data are listed below: 3200 3500 3000 2100 2950 2050 2440 3100 3500 2500

Question 8: Assume that the standard deviation of the salaries was still the same as in 2015. Estimate the average salary (in 2017) with 95% confidence.

Question 9: The assumption made in Question 8 was certainly unrealistic. Estimate the average salary (in 2017) with 95% confidence again assuming that the standard deviation had changed from 2015.

Question 10: Estimate the variance of monthly salaries of Paris residents (in 2017) based on the sample provided above at a 95% confidence level.

Question 11: How would you interpret the result in Question 10 above?

PART 1:

To target the right age-group of people, a marketing consultant must find which age-group purchases from home-shopping channels on TVs more frequently. According to management of TeleSell24/7, a home-shopping store on TV, about 30% of the online-music-downloaders are in their fifties, but the marketing consultant does not believe in that figure. To test this he selects a random sample of 256 online-music-downloaders and finds 64 of them are in their fifties.

1. The value of the test-statistic is: Answer to 2 decimal places.

PART 2:

The following two-way table of counts summarizes whether respondents smoked or not and whether they have had ever divorced or not for persons who had ever been married.

1. Among those who smoked, what percentage has ever been divorced? [Answer to 2 decimal places. Do not type % symbol in the box.]  %

2. Among those who has ever been divorced, what percentage smoked? [Answer to 2 decimal places. Do not type % symbol in the box.]  %

Next we intend to test if smoking habits and being divorced are related or not.
3. What is the expected frequency of smoker and ever being divorced? [Answer to 2 decimal places.]

4. What is the expected frequency of smoker and never being divorced? [Answer to 2 decimal places.]

5. What is the expected frequency of non-smoker and ever being divorced? [Answer to 2 decimal places.]

6. What is the expected frequency of non-smoker and never being divorced? [Answer to 2 decimal places.]

7. To test independence between smoking habits and being divorced, what is the value of chi-square test statistic? [Answer to 3 decimal places.]

Suppose we are testing:

Null hypothesis: smoking habit and ever being divorced are not related,
against
Alternative hypothesis: smoking habit and ever being divorced are related.

8. If the p-value associated to the ch-square test-statistics is 0.418 and the level of significance is 5%, what will be your conclusion?
Not enough information to reach a decision
Do not reject null hypothesis
Reject null hypothesis

A local grocery store owner wants to learn more about how many apples patrons buy from his store week to week, and he has asked for your help calculating some probabilities. He tells you that he believes the data to be normally distributed, and that the average amount of apples bought each week is 678.32 lbs. with a standard deviation of 53.98 lbs.

A) What is the probability that the store sells more than 750 lbs. of apples in a week?

B) What is the probability that the store sells less than 500 lbs. of apples in a week?

C) What is the probability that the store sells between 600 and 700 lbs. of apples?

D) What is the probability that the store sells exactly 678.32 lbs. of apples?

Decide whether the experiment is a binomial experiment. If it is not, explain why. You observe the gender of the next 50 babies born at a local hospital. The random variable represents the number of girls.

Suppose 200 subjects are treated with a drug that is used to treat pain and 55 of them developed nausea. Use a 0.01 significance level to test the claim that more than 20​% of users develop nausea. Identify the null and alternative hypotheses for this test. Choose the correct answer below. A. Upper H 0​: pequals0.20 Upper H 1​: pnot equals0.20 B. Upper H 0​: pequals0.20 Upper H 1​: pgreater than0.20 Your answer is correct.C. Upper H 0​: pgreater than0.20 Upper H 1​: pequals0.20 D. Upper H 0​: pequals0.20 Upper H 1​: pless than0.20 Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test is nothing. ​(Round to two decimal places as​ needed.) Identify the p-value as well as the conclusion for hypothesis test.

The statements in this question are based on the following data: X 2:6 2:6 3:2 3:0 2:4 3:7 3:7 PX D 21:2 Y 5:6 5:1 5:4 5:0 4:0 5:0 5:2 PY D 35:3The correlation coefficient .r/ was calculated as 0:327: Identify the incorrect statement.
1. There is a positive relationship between x and y. 2. N y D 5:043 3. The coefficient of determination is 0:5719:
4. The regression coefficient b1 is also positive.
5. Only 10.7% of the variation in y is explained by the variation in x:

6. Seat Belts A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2823 occupants not wearing seat belts, 31 were killed. Among 7765 occupants wearing seat belts, 16 were killed. The claim is that the fatality rate is higher for those not wearing seat belts. Are Seat Belts Effective? Use alpha=0.01 Hint: We are testing for difference between two proportions. Let P1 indicate the proportion of occupants not wearing seat belts, P2 indicate the proportion of occupants wearing seat belts. Here, we would like to see if seat belt is effective. Therefore, the null hypothesis states H0: P1=P2, where the alternative hypothesis states H1: P1>P2, indicating a right tailed test.

3. Safety Helmets A manufacturer of hard safety hats for construction workers is concerned about the mean and the variation of the forces its helmets transmits to wearers when subjected to an external force. The manufacturer has designed the helmets so that the mean force transmitted by the helmets to the workers is 800 pounds (or less) with a standard deviation to be less than 40 pounds. Tests were run on a random sample of n = 40 helmets, and the sample mean and sample standard deviation were found to be 825 pounds and 48.5 pounds, respectively. Do the data provide sufficient evidence, at the α = 0.05 level, to conclude that the population standard deviation exceeds 40 pounds? Hint: We are testing for population variance (single sample). Here, large variance means there is a safety issue. So when we look from the workers’ safety perspective, we would like to see if the variance of force that is transmitted to the workers’ head exceed 402 =1600 pounds. Therefore, the null hypothesis states H0: s2=402 =1600, where the alternative hypothesis states H1: s2 >1600, indicating a right tailed test.

Hill Top Products ran a regression analysis comparing total production and utility costs for the past six months.

18.   To the nearest dollar, what would be the estimated total utility costs if 500 units were produced?

19. The regression analysis shows an R square (R²) of .94. Which of the following statements best describes the meaning of R²?

20. The Maximax, Maximin, & Equally Likely strategies are part of which of the following:

1. Decision making under risk
2. Decision making under certainty
3. Decision making under uncertainty
4. Both b and c
5. Both a and c

21. A decision tree is a diagram consisting of

   A. square decision nodes

         B. circle probability nodes

        C. branches representing decision alternatives/chance events

        D. all of the above

In a test of the effectiveness of garlic for lowering​ cholesterol, 50 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes ​(beforeminus​after) in their levels of LDL cholesterol​ (in mg/dL) have a mean of 3.7 and a standard deviation of 16.6. Construct a 99​% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL​ cholesterol? What is the confidence interval estimate of the population mean mu​?

what does it mean if "your answer is assumed to be rounded to the highest power possible?" How do I input my answer if it is 2.0198??

The annual per capita consumption of bottled water was 33.6 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 33.6 and a standard deviation of 10 gallons.

a. What is the probability that someone consumed more than 44 gallons of bottled water?
b. What is the probability that someone consumed between 30 and 40 gallons of bottled water?
c. What is the probability that someone consumed less than 30 gallons of bottled water?
d. 90% of people consumed less than how many gallons of bottled water?

1. A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a par- ticular time, and let Y denote the number of hoses on the full service island in use that time. The joint pmf of X and Y appears in the accompanying tabulation.

a. WhatisP(X=1andY =1)?

b. ComputeP(X≤1andY ≤1).

c. Compute P(X ̸= 1 and Y ̸= 1).

d. Compute the marginal pmf of X and Y. Using pX(x), what is P(X ≤ 1)?

e. Are X and Y are independent? Explain.

2. Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable – X for the right tire and Y for the left tire, with joint pdf

?K(x2 +y2), 20≤x≤30, 20≤y≤30,

f(x,y) =

0, otherwise

a. What is the value of K?

b. What is the probability that both tires are underfilled?

c. What is the probability that the difference in air pressure between the two tires is at most 2 psi? (Hint: Draw the shaded region first and then find the boundary of the integration.)

d. Determine the marginal pdf of X and Y . e. Are X and Y independent? Explain.
f. Find E(X) and E(Y ).