Question

Assume that women's heights are normally distributed with a mean given by mu = 64.2in and a standard deviation given by sigma = 2.4 in

(a) 1 woman is randomly selected, find the probability that her is less than 65 in.

(b) 33 women are randomly selectedfind the probability that they have a mean height less than 65 in.

Answer 1

The women's heights are normally distributed with a mean given by mu = 64.2in and a standard deviation given by sigma = 2.4 in.

(a) 1 woman is randomly selected, the probability that her is less than 65 in is.

p(X<65) =p((( X-mu)/ sigma) < ( (65-64.2)/2.4)) = p( Z< 0.3333) = 0.6305461

1 woman is randomly selected, the probability that her is less than 65 in is 0.6305

(b) 33 women are randomly selected, then probability that they have a mean height less than 65 in.

p(X<65) =p((( X-mu)/( sigma/sqrt(n))) < ( (65-64.2)/(2.4/sqrt(33))) = p( Z< 1.9149) = 0.9722

The 33 women are randomly selected, then probability that they have a mean height less than 65 in is 0.9722.