Assume that women's heights are normally distributed with a mean given by u=62.6 in and a standard deviation given by σ=1.6 in.

Question

Assume that women's heights are normally distributed with a mean given by u=62.6 in and a standard deviation given by σ=1.6 in.

(a) If 1 woman is randomly selected, find the probability that her height is less than 63 in.

(b) If 38 women are randomly selected, find the probability that they have a mean height less than 63 in.

 

1. the probability is ___- 

 

Answer 1

Use the z-score table for normal probabilities as reference for both parts.

 

The formula for a z-score:  z = (X - μ)/(σ/√n), where μ is the mean, σ is the standard deviation, n is the sample size, and X is the actual height for an individual.

 

A)  z = (63 - 62.6)/(1.6/√1) = 0.4/1.6 = 0.25  ⇒ P(Z<0.25) = 0.5987

 

B)  z = (63 - 62.6)/(1.6/√38) = 0.4/0.26 = 1.54 ⇒ P(Z<1.54) = 0.9382