What's Your Weight? A 2015 Gallup Poll asked a national random sample of 398 adult women to state their current weight. The mean weight in the sample was x = 155. We will treat these data as an SRS from a Normally distributed population with standard deviation = 35.

(a) Give a 95% confidence interval for the mean weight of adult women based on these data.

(b) Do you trust the interval you computed in part (a) as a 95% confidence interval for the mean weight of all U.S. adult women? Why or why not?