(confidence intervals)

Eccolais a high-end restaurant serving delicious Italian inspired three course meals. They are gathering data on the duration people spend dining at their restaurant. Their goal is to determine the length of time that should be allocated for a table reservation when people book online before making the table available again for the next sitting.Eccolacollected a random sample of 50 reservation durations and calculated the average duration to be 1.5 hours with a standard deviation of 30 minutes.

(a) (5 marks)Construct and interpret a 99% confidence interval for the population mean duration of a reservation at the restaurant.

(b)(2 marks)The restaurant is planning on allowing only 1 hour and 40 minutes per reservation including 10 minutes for clean-up. Explain using the results in (a) if this average time frame would be acceptable? If not, then what should be the recommended average time frame for the duration of a reservation?