Previous records have shown that the number of cars entering Bampor on any day has mean 352 and variance 121.

a) Find the probability that the mean number of cars entering Bampor during a random sample of 200 days is more than 354.

b) State, with a reason, whether it was necessary to assume that the number of cars entering Bampor on any day has a normal distribution in order to find the probability in part (a).

c) It is thought that the population mean may recently have changed. The number of cars entering Bampor during the day was recorded for each of a random sample of 50 days and the sample mean was found to be 356. Assuming that the variance is unchanged, test at the 5% significance level whether the population mean is still 352.