Following are the number of miles traveled for 30 randomly selected business flights within the United States during 1999.

823, 1418, 789, 1758, 2030, 1350, 840, 1656, 1163, 1435,
1146, 1656, 1758, 1418, 823, 1350, 857, 1316, 1843, 1894,
1894, 1095, 1656, 1673, 1401, 1469, 1911, 1146, 721, 653

a) Use the data to obtain a point estimate for the population mean number of miles traveled per business flight, $\mu$, in 1999.
Note: The sum of the data is 40942.
$\bar{x} =$

b) Determine a 95.44% confidence interval for the population mean number of miles traveled per business flight in 1999. Assume that $\sigma= 450$ miles. Confidence interval: (, ).

c) Must the number of miles traveled per business flight in 1999 be exactly normally distributed for the confidence interval that you obtained in part (b) to be approximately correct?

d) What theorem helped you answer part (c)?