The lengths of great white sharks (Carcharodon carcharias) recently spotted near Amity Island have mean of 25 feet and standard deviation of 2 feet. If a random sample of 64 of these sharks is selected, answer the following questions:

20. What is the distribution of the sample mean X ?

(a) binomial (b)approximately normal (c) normal (d) none of these

21. What is the mean of the distribution of the sample mean X ?

(a) 23 (b) 64 (c) 25 (d) 2 (e) 10

22. What is the standard deviation of the distribution of the sample mean X ?

(a) 2 (b) 0.25 (c) 0.5 (d) 25 (e) 23

23. What is the approximate probability that the sample mean X

will be between 24 feet and 26 feet?

(a) 19.15% (b) 68.27% (c) 95.45% (d) 99.73% (e) 99.99%

24. What is the 75th percentile of the distribution of the sample mean X ?

(a) 26.35 feet (b) 25.17 feet (c) 25 feet (d) 75% (e) 75 feet

Use the following information to answer the next 5 questions. John guesses randomly at five multiple choice problems on an exam. Each problem has three potential answers.

25. This scenario can be modeled as a

(a) binomial experiment with 5 trials and success probability of 1/5 per trial. (b) binomial experiment with 5 trials and success probability of 1/3 per trial. (c) normal experiment with 5 trials and success probability of 1/3 per trial. (d) binomial experiment with 3 trials and success probability of 1/3 per trial. (e) binomial experiment with 3 trials and success probability of 1/5 per trial.

26. Complete the following table that represents the probability distribution of X = the number of questions John guesses correctly.

x	0	1	2	3	4	5
P (X = x)

(a) 0.1667, 0.1667, 0.1667, 0.1667, 0.1667, 0.1667

(b)	0.1317,	0.4609,	0.7901, 0.9547, 0.9959, 1
(c)	0.1681,	0.3602,	0.3087,	0.1323,	0.0284,	0.0024
(d)	0.1317,	0.3292,	0.3292,	0.1646,	0.0412,	0.0041
(e)	0.1681,	0.5282,	0.8369,	0.9692,	0.9976,	1

27. What is the probability he will answer at most 1 question correctly?

(a) 2/5 (b) 2/6 (c) 1/6 (d) 0.3292 (e) 0.4609

28. What is the expected number of questions he will answer correctly?

(a) 5/3 (b) 3/5 (c) 1 (d) 1.96 (e) 2

29. What is the standard deviation of the number of questions he will answer correctly?

(a) 1 (b) 1.05 (c) 1.11 (d) 1.29 (e) 2.78