6 On arrival at a business centre, all visitors are required to register at the reception desk. An analysis of the register, for a random sample of 100 days, results in the following information on the number, \(X\), of visitors per day.

1. Calculate an estimate of:
   1. \(\mu\), the mean number of visitors per day;
   2. \(\sigma\), the standard deviation of the number of visitors per day.
2. Give a reason, based upon the data provided, why \(X\) is unlikely to be normally distributed.
3. 1. Give a reason why \(\bar { X }\), the mean of a random sample of 100 observations on \(X\), may be assumed to be normally distributed.
   2. State, in terms of \(\mu\) and \(\sigma\), the mean and variance of \(\bar { X }\).
4. Hence construct a \(99 \%\) confidence interval for \(\mu\).
5. The receptionist claims that she registers on average more than 30 visitors per day, and frequently registers more than 50 visitors on any one day. Comment on each of these two claims.