A battery company claims that its AA batteries last an average of 16 hours with a standard deviation of 1.5 hours. A consumer organization tests this claim by selecting a random sample of 50 AA batteries and draining them under typical conditions. The mean from this sample is x-bar = 15.74 hours. (a) What is the shape of the sampling distribution of the sample mean x-bar for samples of 50 randomly selected batteries? Justify your answer.

(b) Assuming the company’s claim is true, what are the mean and standard deviation of the sampling distribution of the sample mean x-bar for samples of 50 randomly selected batteries?

(c) Assuming the company’s claim is true, how likely is it to get a sample mean of 15.74 hours or less in a random sample of 50 AA batteries?

(d) Based on your answer to part (c), what do you conclude about the company’s claim? Explain.