Question

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

Heights of men and women in the U.S. are normally distributed. Recent information shows:.

Adult women heights: µ = 64.1 inches with ? = 2.7 inches.

Female

5. (a) What percent of women are shorter than 64 inches?

(b) In a group of 250 U.S. women, approximately how many women would be shorter than 64 inches? (give a whole number answer)

6. Find the female height of the U.S. population that represents the 72nd percentile.

7. Find the cutoff height to be in the top 10% of female heights in the U.S.

8. The middle 75% of U.S. women will be between ______ inches and ______ inches tall.

9. Recall from Chapter 2 that values outside of 2 standard deviations are considered to be unusual. A woman in the U.S. shorter than ______ inches would be considered “unusually short”.

10. Suppose a sample of 45 females was randomly selected from the U. S. population.

a. Use the Central Limit Theorem to find ?????

b. Use the Central Limit Theorem to find ????? (3 decimal places)

c. Find P(???>65 inches).

Answer 1

Result:

Heights of men and women in the U.S. are normally distributed. Recent information shows:.

Adult women heights: µ = 64.1 inches with ? = 2.7 inches.

Female

5. (a) What percent of women are shorter than 64 inches?

Z value for 64, z =(64-64.1)/2.7 = -0.04

P( x <64) = P( z < -0.04)

=0.484

(b) In a group of 250 U.S. women, approximately how many women would be shorter than 64 inches? (give a whole number answer)

P( x <64) = P( z < -0.04) = 0.484

Number of women would be shorter than 64 inches = 250*0.484

=121

6. Find the female height of the U.S. population that represents the 72nd percentile.

Z value of 72nd percentile =0.583

X= mean+z*sd = 64.1+0.583*2.7

=65.6741

7. Find the cutoff height to be in the top 10% of female heights in the U.S.

Z value for top 10%=1.282

X= mean+z*sd = 64.1+1.282*2.7

=67.5614

8. The middle 75% of U.S. women will be between 60.995 inches and 66.4 inches tall.

Z values for middle 75% is -1.15 and 1.15

Lower x value = 64.1-1.15*2.7=60.995

upper x value = 64.1+1.15*2.7=66.4

9. Recall from Chapter 2 that values outside of 2 standard deviations are considered to be unusual. A woman in the U.S. shorter than 58.7 inches would be considered “unusually short”.

x value = 64.1-2*2.7=58.7

10. Suppose a sample of 45 females was randomly selected from the U. S. population.

a. Use the Central Limit Theorem to find mean =64.1

b. Use the Central Limit Theorem to find sd=0.402 (3 decimal places)

sd/sqrt(n) = 2.7/sqrt(45) =0.402492

c. Find P(???>65 inches).

Z =(65-64.1)/0.402 =2.24

P( mean x > 65) = P( z > 2.24)

=0.0125