We’re All Nuts, Inc. sells bags of cashews that are advertised as holding 15 oz. of nuts. The quality control manager at the manufacturing plant is responsible for ensuring that the mean weight of bags is at least 15 oz. Twice a week he takes a random sample of 16 bags (from one day’s production—about 10,000 bags) and weighs the nuts in each bag. One day he finds that the mean weight is 14.6 oz. with a standard deviation of 0.6 oz. Below is a dot plot of the sample. (a) Describe the distribution of the weights of the bags of cashews in this sample.

(b) Construct and interpret a 99% confidence interval for the mean weight of cashews in one bag.

(c) Suppose the (population) mean weight in the bags really is 15 ounces and the (population) standard deviation is 0.75 ounces and that the weights are Normally distributed. What is the probability that the means of two independent samples of 16 bags will differ by less than 1 ounce?