The weight of a product is normally distributed with a stand

The weight of a product is normally distributed with a standard deviation of .5 ounces. What should the average weight be if the production manager wants no more than 10% of the products to weigh more than 5.8 ounces?

Solution

The z-score that corresponds to the 90-th percentile is 1.28. Hence, if no more than 10% of the products need to weigh more than 5.8 ounces, then if we let the mean be x, we have that

x + 1.28(0.5) = 5.8

Solving for x gives that the mean needs to be 5.16 ounces.