Let x represent the weight loss, in pounds, of people attending a national weight-loss clinic. The distribution of x has mean 8 pounds and standard deviation 4 pounds. Suppose that a group of 50 people who attend this weight-loss clinic are randomly selected, and let x represent the average weight loss for this group.

a sentence that explains why the sampling distribution of x is approximately normal.

(b) Compute the mean (x) and standard deviation (x) for the sampling distribution of x. Round to four decimal places.

(c) If a group of 50 people who attend this weight-loss clinic are randomly selected, what is the probability that the mean weight loss for the group is between 7.5 and 8.5 pounds? Round to four places.

(d) If a group of 50 people who attend this weight-loss clinic are randomly selected, what is the probability that the mean weight loss for the group is more than 9.5 pounds? Round to four places.

3. A large gas station chain reports that the amount of gasoline purchased per visit, x, is normally distributed with standard deviation = 2 gallons. Suppose that a random sample of 25 purchases at this station is selected. The sample average is 12.4 gallons.

(a) Does the sampling distribution of x follow a normal distribution? Explain why or why not.

(b) Based on the information provided, should a z-interval or t-interval be used when constructing a confidence interval for ? Explain your choice.

(c) Compute a 95% confidence interval for . Round to four places.

(d) What is the margin of error for the interval estimate? Round to four places. (e) An executive from this gas station chain claims that, on average, customers purchase 15 gallons of gas per visit. Is this claim supported by the data? In a sentence, explain why or why not.