# Counting, probability and normal probability plot

(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.

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#### Solution Summary

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.

Z scores

6.18 Many manufacturing processes use the term work-in-process (often abbreviated as WIP). In a book manufacturing plant, the WIP represents the time it takes for sheets from a press to be folded, gathered, sewn, tipped on end sheets, and bound. The following data (stored in the file wip.xls) represent samples of 20 books at each of two production plants and the processing time (operationally defined as the time, in days, from when the books came off the press to when they were packed in cartons) for these jobs:

For each of the two plants, decide whether the data appear to be approximately normally distributed by

a. Comparing data characteristics to theoretical properties.

b. Constructing a normal probability plot.

6.22 The following data, stored in the file utility.xls, represent the electricity costs in dollars, during July 2006 for a random sample of 50 two-bedroom apartments in a large city:

Decide whether the data appear to be approximately normally distributed by

a. Comparing data characteristics to theoretical properties.

b. Constructing a normal probability plot.

6.27 The scheduled commuting time on the Long Island Rail Road from Glen Cove to Ney York City is 65 minutes. Suppose that the actual commuting time is uniformly distributed between 64 and 74 minutes. What is the probability that the commuting time will be

a. less than 70 minutes?

b. between 65 and 70 minutes?

c. greater than 65 minutes?

d. What are the mean and standard deviation of the commuting time?