Assume that women\'s heights are normally distributed with a mean given by ?-64.
ID: 3053826 • Letter: A
Question
Assume that women's heights are normally distributed with a mean given by ?-64.5 in, and a standard deviation given by ? = 2.2 in. a. If 1 woman is randomly selected, find the probability that her height is between 63.8 in and 64.8 in. The probability is approximately .1791. (Round to four decimal places as needed.) b. If 17 women are randomly selected, find the probability that they have a mean height between 63.8 in and 64.8 in. The probability is approximately (Round to four decimal places as needed.)Explanation / Answer
Solution:- Given that ? = 64.5 ? = 2.2
a) P(63.8 < x < 64.8) = P((63.8-64.5)/2.2 < (x - ?)/? < (64.8-64.5)/2.2)
= P(-0.3182 < Z < 0.1364)
= 0.1812
b) n = 17
P(63.8 < x < 64.8) = P((63.8-64.5)/(2.2/sqrt(17)) < (x - ?)/(?/sqrt(n)) < (64.8-64.5)/(2.2/sqrt(17))
= P(-1.3119 < Z < 0.5622)
= 0.6172