According to a General Social Survey, in the United States the distribution of y = number of good friends (not including family members) has a mean of 5.5 and a standard deviation of 3.9.

Suppose these are the population mean and standard deviation.

(a) Does y have a normal distribution? Explain.

(b) For a random sample of 819 adults (the size of the GSS for this variable), describe the sampling distribution of ¯y by giving its shape, mean, and standard error.

(c) Refer to (b). Report an interval within which the sample mean would almost surely fall.