(c) Find the probability that his height is more than 72 inches. (d) Can any of
ID: 2934144 • Letter: #
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
Ans:
Given that
mean=64.3
standard dev=2.6
z=(x-mean)/std dev=(x-64.3)/2.6
a)
z=(56.5-64.3)/2.6=-3
P(x<56.5)=P(z<-3)=0.0013
b)when x=61
z=(61-64.3)/2.6=-1.27
when x=67
z=(67-64.3)/2.6=1.04
P(61<=x<=67)=P(-1.27<=z<=1.04)
=P(z<=1.04)-P(z<=-1.27)
=0.8508-0.1020
=0.7488
c)
z=(70.5-64.3)/2.6=2.38
P(z>2.38)=1-P(z<=2.38)=1-0.9913=0.0087
d)As,the probability of being less than 56.5 is 0.0013,which is less than 0.05,so it is unusual event.
and
probability of being greater than 70.5 is 0.0087,which is less than 0.05,so it is unusual event.
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