Background: A potato chip manufacturer was having problems with the Weights and Measures inspectors after the inspectors found some bags containing less than the required 42.5 grams (formerly 1.5 ounces) of chips. In response, the manufacturer had increased the weight setting on the bagging machines to 50 grams, but were now over-packing the bags and, consequently, giving away chips. A random sample of bags were taken off the line and the chips in the bags were carefully weighed, as shown in the attached table.

Question: Suppose the population weight is indeed 42.5 gram, then according to the Three Rules of Thumb, the probability to observe the sample mean as calculated above is less than ? .

Note: My answer for this question was 34% and was marked incorrect. My answers for the sample mean (49.66) and standard deviation and (3.67) were marked correct. I calculated the sample mean to be approximately 1.95 standard deviations (in other words, less than two) from the mean of 42.5. I believe the answer is 2.5% (based on other homework assignments on this site) but I don't know why.

Here is the full table if you need it.