(a) The financial database of a company is secured by a password protection system. Each employee is given a randomly generated password containing three letters and two numbers. If repetitions of letters and numbers are not allowed, how many possible passwords are there?
(b) Tickets for international cricket matches between Australia and England are very popular. The ticket sales manager needs to have enough sales staff available when the ticket office opens to cope with the influx of cricket fans. Past experience shows that fans will arrive at a rate of 15 per minute. Find the probability that 20 or more fans will arrive in a given minute?
(c) A couple who own and manage a convenience store have been feeling pressure since a new low-price supermarket opened just down the road. In the year since the supermarket's opening, the couple have noticed a drop in their daily takings. The results of a random sample of daily takings for fifty days (all drawn from the past year) are listed below (expressed in whole dollars).
(see attached file for data)
Test this data using the normal probability plot to see whether it can adequately be described by the normal distribution.
The solution gives detailed steps on solving 3 questions: one is for counting, one is for probability under Poissson distribution, and one is for a normal probability plot.