The owner of a restaurant that serves continental food wants to study characteristics of her customers. She decides to focus on two variables: the amount of money spent by customers and whether customers order dessert. The mean and the standard deviation of amount spent for a simple random sample of 16 customers is found to be Rs. 500 and Rs. 20 respectively.

a) Construct a 98% confidence interval estimate of the population mean amount spend per customer in the restaurant.

b) based on the past experience, the owner of the restaurant believes that 80% of the customers order for dessert. If on a day 225 customers visit the restaurant, what is the probability that at least 84% of them would order for dessert.