4 A very popular play has been performed at a London theatre on each of 6 evenings per week for about a year. Over the past 13 weeks ( 78 performances), records have been kept of the proceeds from the sales of programmes at each performance. An analysis of these records has found that the mean was \(\pounds 184\) and the standard deviation was \(\pounds 32\).

1. Assuming that the 78 performances may be considered to be a random sample, construct a \(90 \%\) confidence interval for the mean proceeds from the sales of programmes at an evening performance of this play.
2. Comment on the likely validity of the assumption in part (a) when constructing a confidence interval for the mean proceeds from the sales of programmes at an evening performance of:
   1. this particular play;
   2. any play.