Bags of a certain brand of potato chips say that the net weight of the contents

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.

Does the sample provide strong evidence that the mean weight of the bags is lower than the 35.6 grams listed on the package?

Explanation / Answer

probability that a random sample of 35 bags has a mean weight of 33.6 grams or less:

as probability of that happing is very small terefore it  provide strong evidence that the mean weight of the bags is lower than the 35.6 grams listed on the package.

for normal distribution z score =(X-)/ here mean=       = 35.600 std deviation   == 5.2000 sample size       =n= 35 std error=x=/n= 0.8790

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