(c) Find the probability that his height is more than 72 inches. (d) Can any of

Question

(c) Find the probability that his height is more than 72 inches. (d) Can any of these events be considered unusual? Explain your reasoning. 14. Heights of Women A survey was conducted to measure the heights of U.S women. In the survey, respondents were grouped by age. In the 20-29 age group, the heights were normally distributed, with a mean of 64.3 inches and a standard deviation of 2.6 inches. A study participant is randomly selected (Adapted from U.S. National Center for Health Statistics) (a) Find the probability that her height is less than 56.5 inches. (b) Find the probability that her height is between 61 and 67 inches. (c) Find the probability that her height is more than 70.5 inches (d) Can any of these events be considered unusual? Explain your reasoning

Explanation / Answer

= 64.3 = 2.6

(a) X = 56.5

Z = (X - ) /

= (56.5 - 64.3) / 2.6

= -3

Probability from table = 0.0013.

(b) 61 < X < 67

Probability P(61 < X < 67) = P(Z < 67) - P(Z < 61)

= P(Z < (67 - 64.3) / 2.6) - P(Z < (61 - 64.3) / 2.6)

= P(Z < 1.0384) - P(Z < -1.269)

= 0.8505 - 0.1022

= 0.7483.

(c) X = 70.5

Z = (70.5 - 64.3) / 2.6

= 2.3846.

P(Z > 2.3846) = 0.0085.

(d) The result is part (a) is less than 0.05 and can be deemed unusual. The other two values are greater than 0.05 and cannot be considered unusual.

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