# Statistics homework

**Directions:**

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

Adult men heights: μ = 69.6 inches with σ = 3 inches.

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

*Use the above information to answer all questions (except those marked with an asterisk *). Probabilities should be 4 decimal places, but z-scores and x-values should be given to 2 decimal places. Use our* class sample *data below to answer questions marked with an asterisk *.*

**Female Data Questions**

1. (a) If a woman is selected at random from the U.S. population, what is the probability that she is taller than 67 inches?

*(b) What % of women in our class data (collected by the class) are taller than 67 inches? (give answer in decimal format rounded to 4 places)

2. (a) If a woman is selected at random from the U.S. population, what is the probability that she is between 61 and 68 inches tall?

*(b) What % of women in our class data are between 61 and 68 inches? (give answer in decimal format rounded to 4 places) (Note: include 61” and 68”).

3. What percent of women in the U.S. are shorter than 5 ft.?

4. What percent of women in the U.S. are taller than 6 ft.?

5. (a) What percent of women are shorter than 63 inches?

(b) In a group of 150 U.S. women, approximately how many women would be shorter than 63 inches? (give a whole number answer)

6. Find the female height of the U.S. population that represents the 62nd percentile.

7. Find the cutoff height to be in the top 8% of female heights in the U.S.

8. The middle 60% 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. taller than ______ inches would be considered “unusually tall”.

10. Suppose a sample of 47 females was randomly selected from the U. S. population.

a. Use the Central Limit Theorem to find 𝜇𝑥̅

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

c. Find P(𝑥̅>64 inches).

**Class Data**

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 | 58 | 5 | 20 | 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 |

46 | F | 65 | 9 | 25 | R |

47 | F | 62 | 7 | 31 | R |

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