Question

MALE :Student # Gender Height Shoe Age Hand

1 M 67 10 19 R

2 M 74 12 17 R

3 M 72 11.5 19 R

4 M 69 10 35 R

5 M 66 9 18 R

6 M 71 10.5 17 R

7 M 72 10.5 17 R

8 M 66 10 20 R

9 M 67 10 18 R

10 M 71 10.5 24 R

11 M 66 10 21 R

12 M 71 10.5 18 R

13 M 69 10 22 R

14 M 66 9.5 18 L

15 M 76 14 18 R

16 M 69 11 22 R

17 M 68 9 19 R

18 M 70 12 30 R

19 M 67 10 24 R

20 M 70 11 21 R

21 M 70 10 52 R

22 M 63 9 27 R

23 M 69 11 22 R

24 M 72 10 22 R

25 M 76 11.5 20 L

26 M 75 11 17 R

27 M 72 11 50 L

28 M 69 11 20 R

29 M 70 12 20 R

30 M 69 11.5 23 R

31 M 70 11 18 R

32 M 67 10 21 R

33 M 68 11 44 R

34 M 76 13 48 R

35 M 62 8 23 L

36 M 69 9 19 R

37 M 72 10 60 R

38 M 73 11.5 41 R

39 M 70 9.5 39 R

40 M 78 15 24 R

41 M 65 8.5 23 R

42 M 68 9.5 20 R

FEMALE: Student # Gender Height Shoe Age Hand

1 F 68 8.5 20 R

2 F 60 5.5 27 R

3 F 64 7 31 R

4 F 67 7.5 19 R

5 F 65 8 20 R

6 F 66 9 29 R

7 F 62 9.5 30 L

8 F 63 8.5 18 R

9 F 60 5 19 L

10 F 63 7.5 42 R

11 F 61 7 20 R

12 F 64 7.5 17 R

13 F 65 8 19 R

14 F 68 8 19 R

15 F 63 7.5 18 R

16 F 62 7.5 19 R

17 F 64 7 23 R

18 F 72 11 28 R

19 F 62 8 20 R

20 F 59 6.5 29 R

21 F 64 8.5 19 R

22 F 68 9.5 23 R

23 F 65 9.5 34 R

24 F 63 8 27 R

25 F 65 8 23 R

26 F 62 7.5 30 R

27 F 67 7.5 31 L

28 F 66 9 37 R

29 F 61 6 24 R

30 F 61 6.5 46 R

31 F 68 8 20 R

32 F 63 7.5 42 R

33 F 63 5.5 33 R

34 F 63 9 35 R

35 F 65 8 44 R

36 F 69 9 28 R

37 F 68 9 20 R

38 F 63 7 49 R

39 F 62 6.5 19 R

40 F 66 7.5 19 R

41 F 69 7.5 55 R

42 F 69 11 40 R

43 F 63 6.5 19 R

44 F 61 7.5 20 R

45 F 68 9 19 R

Round 4 decimal places or give answers in scientific notation if necessary.

1. It is believed to be true that 15% of the U.S. population is left-handed. You randomly select 8 people. Let x represent the number of left-handers.

a. Construct a binomial distribution. (4 decimal places or give answers in scientific notation if necessary.)

b. Find the probability that exactly 6 people are left-handed.

c. Find the probability that less than 3 people are left-handed.

d. Find the probability that at least 1 person is left-handed.

e. Find the mean of the binomial distribution.

f. Find the standard deviation of the binomial distribution.

2. Complete the following sentence:

a. In our SCC class data, we surveyed a TOTAL (males and females) of _____ (n) students and found that _____ (x) were left-handed.

b. Assuming that 15% of the population is left-handed, find the probability of surveying n students and getting exactly x “lefties” (Use the numeric values for n and x from our SCC class data.)

c. In chapter 3, we noted that an event that occurs with a probability of 0.05 or less is considered unusual. Is the number of “lefties” (x) in our data unusual? (State yes or no)

d. Assuming that 15% of the population is left-handed and we surveyed a total of (n) students, calculate the mean.

e. Using the mean from part d, should we have expected more or less “lefties” in our SCC class data?

Answer 1

1. It is believed to be true that 15% of the U.S. population is left-handed. You randomly select 8 people. Let x represent the number of left-handers.

a. Construct a binomial distribution. (4 decimal places or give answers in scientific notation if necessary.)

Here X has binomial distribution with parameters n=8 and p=0.15. The pdf is

b. Find the probability that exactly 6 people are left-handed.

c. Find the probability that less than 3 people are left-handed.

d. Find the probability that at least 1 person is left-handed.

e. Find the mean of the binomial distribution.

The mean is

f. Find the standard deviation of the binomial distribution.