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- September 13, 2020
- By menge

hey I see that you answered these questions on oct 11, I am not able to view the all the answers can you send me the completed answer sheet

1. True or False. Justify for full credit. (15 pts)

(a) If the variance of a data set is zero, then all the observations in this data set are zero.

(b) If P(A) = 0.4 , P(B) = 0.5, and A and B are disjoint, then P(A AND B) = 0.9.

(c) Assume X follows a continuous distribution which is symmetric about 0. If , then .

(d) A 95% confidence interval is wider than a 90% confidence interval of the same parameter.

(e) In a right-tailed test, the value of the test statistic is 1.5. If we know the test statistic follows a

Student?s t-distribution with P(T < 1.5) = 0.96, then we fail to reject the null hypothesis at 0.05 level of

significance .

The frequency distribution below shows the distribution for checkout time (in minutes) in UMUC

MiniMart between 3:00 and 4:00 PM on a Friday afternoon.

Checkout Time (in minutes)

Checkout Time (in

minutes) Frequency 1.0 – 1.9 3 2.0 – 2.9 Relative

Frequency 12 3.0 – 3.9

4.0 – 4.9 0.20

3 5.0 -5.9

Total 25 2. Complete the frequency table with frequency and relative frequency. Express the relative frequency to

two decimal places. (5 pts)

3. What percentage of the checkout times was at least 3 minutes? (3 pts)

4. In what class interval must the median lie? Explain your answer. (5 pts)

5. Does this distribution have positive skew or negative skew? Why? (2 pts) Refer to the following information for Questions 6 and 7. Show all work. Consider selecting one card at a

time from a 52-card deck. (Note: There are 4 aces in a deck of cards)

6. If the card selection is without replacement, what is the probability that the first card is an ace and the

second card is also an ace? (Express the answer in simplest fraction form) (5 pts)

7. If the card selection is with replacement, what is the probability that the first card is an ace and the

second card is also an ace? (Express the answer in simplest fraction form) (5 pt The five-number summary below shows the grade distribution of two STAT 200 quizzes for a sample of

500 students. Q1 Median Q3 Maximum Minimum

Quiz 1 15 30 55 85 100 Quiz 2 20 35 50 90 100 For each question, give your answer as one of the following: (a) Quiz 1; (b) Quiz 2; (c) Both quizzes have

the same value requested; (d) It is impossible to tell using only the given information. Then explain your

answer in each case. (4 pts each)

8. Which quiz has less interquartile range in grade distribution?

9. Which quiz has the greater percentage of students with grades 80 or over?

10. Which quiz has a greater percentage of students with grades less than or equal to 50?

Refer to the following information for Questions 11, 12, and 13. Show all work. Just the answer, without

supporting work, will receive no credit.

There are 1000 students in a high school. Among the 1000 students, 800 students have a laptop, and 300

students have a tablet. 250 students have both devices.

11. What is the probability that a randomly selected student has neither device? (10 pts)

12. What is the probability that a randomly selected student has a tablet, given that he/she has a laptop?

(5 pts) 13. Let event A be the selected student having a laptop, and event B be the selected student having a

tablet. Are A and B independent events? Why or why not? (5 pts)

14. A combination lock uses three distinctive numbers between 0 and 39 inclusive. How many different

ways can a sequence of three numbers be selected? (Show work) (5 pts)

15. Let Let random variable x represent the number of heads when a fair coin is tossed three times.

Show all work. Just the answer, without supporting work, will receive no credit.

(a) Construct a table describing the probability distribution. (5 pts)

(b) Determine the mean and standard deviation of x. (Round the answer to two decimal places) (10 pts)

16. Mimi just started her tennis class three weeks ago. On average, she is able to return 25% 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? (5 pts)

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

(Show work) (10 pts)

Refer to the following information for Questions 17, 18, and 19. Show all work. Just the answer,

without supporting work, will receive no credit.

The lengths of mature jalapeño fruits are normally distributed with a mean of 3 inches and a

standard deviation of 1 inch.

17. What is the probability that a randomly selected mature jalapeño fruit is between 1.5 and 3.5

inches long? (5 pts)

18. Find the 90th percentile of the jalapeño fruit length distribution. (5 pts)

19. If a random sample of 400 mature jalapeño fruits is selected, what is the standard deviation of the

sample mean? (5 pts)

20. A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that the population

standard deviation of the lifetime is 500 hours. Construct a 90% confidence interval estimate of the

mean lifetime. Show all work. Just the answer, without supporting work, will receive no credit. (8 pts)

21. Consider the hypothesis test given by 5.0: 5 .0: 10 pH p H

In a random sample of 400 subjects, the sample proportion is found to be . 55.0? p

(a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work,

will receive no credit.

(b) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting

work, will receive no credit.

(c) Is there sufficient evidence to justify the rejection of at the level? Explain. (15 0 H 0.01