Question

you are buying soccer cleats (shoes) for young female soccer players in your league. you know the mean shoe size and the standard deviation of the shoe chest size. roughly what proportion of the shoe sizes of the players would you expect to be within one standard deviation of the mean chest size? choose the best answer.
a. 68% if the shoe size is normally distributed
b. 50% if the shoe size is normally distributed
c. 50% if the mean shoe size is normally distributed
d. 95%
e. 2/3

Explanation:

This relies on the empirical rule (68-95-99.7 rule) for normally distributed data, which states that ~68% of observations fall within 1 standard deviation of the mean. The other options are incorrect: 50% does not match the rule, 95% applies to 2 standard deviations, and 2/3 is an imprecise approximation not tied to the formal normal distribution rule.

Answer:

a. 68% if the shoe size is normally distributed