Question

Bags of a certain brand of potato chips say that the net weight of the contents is 35.6 grams. Assume that the standard deviation of the individual bag weights is 5.2 grams. A quality control engineer selects a random sample of 35 bags. The mean weight of these 35 bags turns out to be 33.6 grams. If the mean and standard deviation of individual bags is reported correctly, what is the probability that a random sample of 35 bags has a mean weight of 33.6 grams or less.

Answer 1

Sample size = 35

So we can use central limit theorem to obtained the sampling distribution of sample mean( ).

The sampling distribution of sample mean( ) is approximately normal with mean 35.6, and standard deviation as

Here we want to find P( < 33.6 )

Let's use excel:

P( < 33.6 ) = "=NORMDIST(33.6,35.6,0.879,1)" = 0.011444

So that the probability that a random sample of 35 bags has a mean weight of 33.6 grams or less is 0.011444