So i have to use the empirical rule thing to solve this but i need showing the work

a shoe manufacturer collected data regarding men’s shoe size and found that they are normally distributed. if the mean shoe size is 11 and the standard deviation is 1.5, find the probability that a man’s shoe size is greater than or equal to 12.5.

16%

Step-by-step explanation:

First, calculate the z-score.

z = (x − μ) / σ

where x is the value,

μ is the mean,

and σ is the standard deviation.

z = (12.5 − 11) / 1.5

z = 1

What this means is that 12.5 is 1 standard deviation above the mean.

According to the empirical rule, 68% of a normal distribution is between -1 and +1 standard deviations.  That means 32% is outside of that range.  Since normal distributions are symmetrical, we can say that 16% is less than -1 standard deviations, and 16% is greater than +1 standard deviations.

Therefore, the probability that a man's shoe is greater than or equal to 12.5 (greater than +1 standard deviations) is 16%.