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Quantitative Methods

QMS 102

Changping Wang

Winter

Description

Business Statistics I QMS102 - Test 2
REVIEW PROBLEMS
Question 1
Table 2- Household expenditures, by selected metropolitan area
(Halifax, Saint John) 2007
Halifax Saint John
Expenditures per household Expenditures per household
$ $
Food 7,198 7,073
Shelter 13,337 11,745
Household Operation 3,547 3,138
Household furnishing and 2,055 1,541
equipment
Clothing 2,936 2,717
Transportation 9,357 10,745
Health care 1,903 2,044
Personal care 1,232 1,011
Recreation 3,989 3,458
Reading materials and other 277 224
printed matter
Education 1,605 981
Tobacco products and 1,692 1,471
alcoholic beverages
Games of chance (net 232 157
amount)
Miscellaneous 1,071 1,007
Personal income taxes 13,848 14,198
Personal insurance 4,236 4,351
payments and pension
contributions
Gifts of money and 2,446 1,388
contributions
Source:Statistics Canada, CANSIM, table (for fee) 203-0001 and Cataogue no.
62F0026MIE
Last modified: 2008-12-22
Refer to Table 2 which contains the “Household expenditures, by selected metropolitan area:
(Halifax, Saint John)” data that was published by Statistics Canada.
Part (I) Assist the statistician to construct a box whisker plot for the data on ``Expenditures
per household living in Halifax’’ by computing the following: 1) The mean is 4174.18 .
2) The median is 2446 .
3) The first quartile is 1418.5 .
4) The third quartile is 5717 .
5) The IQR (interquartile range) is 4298.5 .
6) The right inner fence (RIF) is 12164.75 .
7) The right outer fence (ROF) is 18612.5 .
8) The left inner fence (LIF) is -5029.25 .
9) The left outer fence (LOF) is -11477 .
10) The right whisker ends at 9357 .
11) State the value of each outlier: (If there is no outlier, say “none”)
13,337, 13,848 ____________________ .
12) State the value of each extreme: (If there is no extreme, say “none”)
None ____________________ .
Part (II)
a) Based on your answer in part a), would you say that the distribution of the data on the
“expenditures per household living in Saint John’’ is skewed left, symmetric, or
skewed right? Show all work that leads to your answer. Questions 2 - 5 will be based on the following information.
During a normal weekday, customers arrive randomly at a local branch of ScotiaBank in the
downtown Toronto at an average rate of 5 per 3 minutes.
Question 2 What is the probability that there are 10 customers arriving at this branch during
the next 3 minutes? Ans: 0.0181
Question 3 What’s the probability that at least 10 customers arriving at this branch during the
next 6 minutes? Ans: 0.5421
Question 4 What’s the probability that no more than 10 customers arriving at this branch
during the next 12 minutes? Ans: 0.0108
Question 5 How many customers would you expect during the next hour? Ans: 100
Questions 6 – 9 will be based on the following information.
A telephone company has recently performed a detailed analysis of its customers. Some of the
results are mentioned below.
Thirty (30) percent of the customers prefer to pay their bills by using credit cards. Forty-five (45)
percent prefer to pay by cash/debit cards through a local bank, while the remainders prefer to pay
by sending a personal cheque.
Suppose that at the end of a day, 200 payments have been received.
Question 6 What is the probability that more than 50 customers would pay by credit cards?
Ans: 0.9305
Question 7 What is the probability that less than 100 customers would pay by cash/debit
cards? Ans: 0.9113
Question 8 What is the probability that 60 customers would pay by sending cheques? Ans:
0.017
Question 9 How many customers would you expect that they would pay by cash/debit cards?
Ans: 90 Questions 10 - 16 will be based on the following information.
A local Wears store has recently performed a detailed analysis of its customers. Some of the
results are mentioned below.
Of the customers that go shopping in the local Wears store, the average time spent in minutes
was 45 for men and 120 for women. The amounts were normally distributed with a standard
deviation of 10 and 12 for men and women, respectively.
Question 10 What is the probability that a man will spend at most an hour? Ans: 0.9332
Question 11 What is the probability that a woman will spend at least 2 and half hours? Ans:
0.0062
Question 12 What is the probability that a woman will spend less than half an hour? Ans: 0
Question 13 What is the minimum amount (in minutes, rounded to a whole number) of the
highest 65% spent by women? Ans: 115
Question 14 What is the maximum amount (in minutes, rounded to a whole number) of the
lowest 15% spent by men? Ans: 35
Question 15 Suppose that 20 men have gone shopping in this store. What’s the probability
that more than 4 men spent at least 60 minutes? Ans: 0.009
Question 16 Sup

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