Imagine I want to produce apple pies. My pie only tastes good if the apples have an acid content between 500 and 600 (mg/100g). I told a farmer that I will buy his apples if 95% of them have an acidity within these limits.

I am struggling to calculate the number of apples that I would need to test to have a chance of 80% that at least 95% of the farmer’s apples fulfill my acid content criteria.

My approach was to imagine a hypothetical population of apples with a normally distributed acidity with a mean of 550 (mg/100g) and a standard deviation of 51 (mg/100g). I have selected these values so that 95% of the acidity values lie between 500 and 600 (mg/100g).

I should then be able to test if the farmer’s apples are from the same distribution using Kolmogorov-Smirnov. However, I fail to find a way to predict the necessary sample size for this.

Is there are way to calculate the sample size necessary for a Kolmogorov-Smirnov test?

Does my approach make any sense at all?