# 8. Answer the following two questions. (Show all work. Just the answer, without supporting work,…

8. Answer the following two questions. (Show all work. Just the answer, without supporting work,…

8. Answer the following two questions. (Show all work. Just the answer, without supporting work, will receive no credit).

(a) The steering committee of UMUC Green Solutions Team consists of 3 committee members. 10 people are interested in serving in the committee. How many different ways can the committee be selected?

(b) A bike courier needs to make deliveries at 6 different locations. How many different routes can he take?

9. Let random variable x represent the number of girls in a family of three children.

(a) Construct a table describing the probability distribution.

(b) Determine the mean and standard deviation of x. (Round the answer to two decimal places)

10. Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of her opponent’s serves. Assume her opponent serves 10 times.

(a) Let X be the number of returns that Mimi gets. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively?

(b) Find the probability that that she returns at least 1 of the 10 serves from her opponent.

11. A research concludes that the number of hours of exercise per week for adults is normally distributed with a mean of 4 hours and a standard deviation of 3 hours. Show all work. Just the answer, without supporting work, will receive no credit.

(a) Find the 75th percentile for the distribution of exercise time per week. (round the answer to 2 decimal places)

(b) What is the probability that a randomly selected adult has more than 7 hours of exercise per week? (round the answer to 4 decimal places)

12. Based on the performance of all individuals who tested between July 1, 2012 and June 30, 2015, the GRE Verbal Reasoning scores are normally distributed with a mean of 150 and a standard deviation of 8.45. (https://www.ets.org/s/gre/pdf/gre_guide_table1a.pdf). Show all work. Just the answer, without supporting work, will receive no credit.

(a) Consider all random samples of 36 test scores. What is the standard deviation of the sample means?

(b) What is the probability that 36 randomly selected test scores will have a mean test score that is between 148 and 152?

13. An insurance company checks police records on 500 randomly selected auto accidents and notes that teenagers were at the wheel in 80 of them. Construct a 95% confidence interval estimate of the proportion of auto accidents that involve teenage drivers. Show all work. Just the answer, without supporting work, will receive no credit.

14. A city built a new parking garage in a business district. For a random sample of 60 days, daily fees collected averaged \$2,000, with a standard deviation of \$400. Construct a 95% confidence interval estimate of the mean daily income this parking garage generates. Show all work. Just the answer, without supporting work, will receive no credit.

15. A researcher claims the proportion of auto accidents that involve teenage drivers is less than 20%. ABC Insurance Company checks police records on 200 randomly selected auto accidents and notes that teenagers were at the wheel in 32 of them. Assume the company wants to use a 0.05 significance level to test the researcher’s claim.

(a) Identify the null hypothesis and the alternative hypothesis.

(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(c) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.

(d) Is there sufficient evidence to support the researcher’s claim that the proportion of auto accidents that involve teenage drivers is less than 20%? Explain.

16. Mimi was curious if regular excise really helps weight loss, hence she decided to perform a hypothesis test. A random sample of 5 UMUC students was chosen. The students took a 30- minute exercise every day for 6 months. The weight was recorded for each individual before and after the exercise regimen. Does the data below suggest that the regular exercise helps weight loss? Assume Mimi wants to use a 0.05 significance level to test the claim.

(a) Identify the null hypothesis and the alternative hypothesis.

(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(c) Determine the p-value. Show all work; writing the correct critical value, without supporting work, will receive no credit.

(d) Is there sufficient evidence to support the claim that regular exercise helps weight loss? Justify your conclusion.

17. In a pulse rate research, a simple random sample of 100 men results in a mean of 80 beats per minute, and a standard deviation of 11 beats per minute. Based on the sample results, the researcher concludes that the pulse rates of men have a standard deviation greater than 10 beats per minutes. Use a 0.05 significance level to test the researcher’s claim.

(a) Identify the null hypothesis and alternative hypothesis.

(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(c) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.

(d) Is there sufficient evidence to support the researcher’s claim? Explain.

18. The UMUC MiniMart sells five different types of mugs. The manager reports that the five types are equally popular. Suppose that a sample of 500 purchases yields observed counts of 105, 110, 85, 110, and 90 for types 1, 2, 3, 4, and 5, respectively. Use a 0.05 significance level to test the claim that the five types are equally popular. Show all work and justify your answer.

(a) Identify the null hypothesis and the alternative hypothesis.

(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(c) Determine the P-value. Show all work; writing the correct P-value, without supporting work, will receive no credit.

(d) Is there sufficient evidence to support the manager’s claim that the five types of mugs are equally popular? Justify your answer.

19. A STAT 200 instructor believes that the average quiz score is a good predictor of final exam score. A random sample of 10 students produced the following data where x is the average quiz score and y is the final exam score.

(a) Find an equation of the least squares regression line. Show all work; writing the correct equation, without supporting work, will receive no credit.

(b) Based on the equation from part (a), what is the predicted final exam score if the average quiz score is 90? Show all work and justify your answer.

20. A study of 5 different weight loss programs involved 200 subjects. Each of the 5 programs had 40 subjects in it. The subjects were followed for 12 months. Weight change for each subject was recorded. We want to test the claim that the mean weight loss is the same for the 5 programs.

(a) Complete the following ANOVA table with sum of squares, degrees of freedom, and mean square (Show all work):

(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(c) Determine the P-value. Show all work; writing the correct P-value, without supporting work, will receive no credit.

(d) Is there sufficient evidence to support the claim that the mean weight loss is the same for the 5 programs at the significance level of 0.05? Explain.

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8. Answer the following two questions. (Show all work. Just the answer, without supporting work,…