A manufacturer claims that the mean weight of its ice cream cartons is 12 ounces with a standard deviation of 0.5 ounce. Assume the weights are normally distributed. You test 25 cartons and find their mean weight to be 12.22 ounces.
(a) Assuming the manufacturer's claim is correct, what is the probability the mean of the sample is 12.22 ounces or more?
(b) Using your answer form part (a), what do you think of the manufacturer's claim?
(c) Would it be unusual to have an individual carton with a weight of 12.22 ounces? Why or why not?