A random sample of gasoline sales to 16 cars shows an average sale of 34.78 liters and sample standard deviation of 10.58 liters.

a) Estimate the population variance of gasoline sales with a 95% confidence interval.

b) Construct 99% confidence interval for the population mean of gasoline sales.

c) What assumptions is necessary for your answers to be valid in parts (a) and (b).

d) Compose the variable used to obtain confidence interval in part (a). What is the probability distribution of this variable?