Question

Assume that​ women's heights are normally distributed with a mean given by u equals 64.2 inμ=64.2 in​, and a standard deviation given by σ=2.7 in.

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

​(b) If 45 women are randomly​ selected, find the probability that they have a mean height less than 65 in.

Answer 1

Solution :

Given that ,

mean = = 64.2

standard deviation = = 2.7

(a)

P(x < 65) = P[(x - ) / < (65 - 64.2) / 2.7]

= P(z < 0.2963)

= 0.6165

Probability = 0.6165

(b)

= / n = 2.7 / 45 = 0.4025

P( < 65) = P(( - ) / < (65 - 64.2) / 0.4025)

= P(z < 1.9876)

= 0.9766

Probability = 0.9766