Answer to Question #117255 in Statistics and Probability for Michael

Question

A men’s shoe designer is willing to accommodate 95% of the male population. If the mean foot length is 25.25 cm and the standard deviation is 3.875 cm, answer the following

Q1. What is the smallest foot length the designed is willing to accommodate ?
Q2. What is the largest foot length the designed is willing to accommodate

Answer 1

Based on the 95% Rules, we have:

Moving 2 standard deviations to right of the mean and also to the left of the mean, we cover 95% of values. So we conclude:

 the smallest foot length the designed is willing to accommodate =

μ−2σ = 25.25 - 2*(3.875) = 17.5 

 the largest foot length the designed is willing to accommodate = μ+2σ = 25.25+2*(3.875) = 33