STATISTICS FOR MANAGEMENT I
December 17, 2007, 7.00-10.00pm Gym DEF
Professors: Khoroshilov, Phansalker, Wright
Time allowed: 3 hours.
Closed book exam
First Name ..........................................................
Last Name ..........................................................
Student Number .................................................
Students can obtain full marks (50) by answering questions 1 – 5
Bonus marks (7.5) are available from questions 6 - 8
All questions are to be answered on the answer sheet in the space given.
The back of the question paper should be used for rough work only.
1 Qu. #1. A telecommunications equipment vendor produces two lines of products (i)
private network equipment and (ii) public network equipment. It estimates the market
size for these two product lines in one year’s time as shown in the table:
Estimated Market Size: $bn
Mean Standard Deviation
Private Network 7.6 1.2
Public network 4.3 0.5
(3) (a) Assuming that the markets for the two lines of products are independent of each
other, calculate the mean and standard deviation of the estimated total market size in one
(4) (b) In fact, the correlation between the two markets is 0.47. (I.e. correlation
coefficient = 0.47). Calculate the mean and standard deviation of the estimated total
market size in one year’s time.
(3) (c) The Vice President of the Private Network Equipment Division wants to be at
least 87.5% sure of having enough capacity to meet estimated market size next year. We
do not know the shape of the distribution of market size but we do know that the
distribution is symmetric. What market size figure in $bn should the Vice President plan
for, so as to be at least 87.5% sure the actual market will be lower than this figure?
Qu. #2. A large survey of customers who called a customer service toll-free telephone
number found that 46% of customers were satisfied with the service they received. Since
the survey, the customer service agents have received additional training. After the
training, interviews with 10 randomly selected customers found that 6 of them were
satisfied with the service they received.
(3) (a) What is the probability that 6 out of 10 randomly selected customers would
have said they were satisfied with the service they received, before the training.
(5) (b) What is the probability that 60 or more out of 100 randomly selected
customers would have said they were satisfied with the service they received,
before the training. (Hint: Use continuity correction.)
(2) (c ) Do you think the training has improved customer satisfaction. State your
reasons in two short sentences.
Qu. #3. Gasprom and United Energy System (UES) are the two largest energy (oil, gas,
and electricity) companies in Russia. The annual return on Gasprom shares is normally
distributed with mean of 15% and a standard deviation of 25%. Return on the UES shares
is also normally distributed. However, since the UES has higher debt-equity ratio, its
shares have a higher expected return of 20% and a higher standard deviation of 35%. For
simplicity, assume that stock returns are independent.
(2) (a) What is the probability that you will get a positive return on any money invested
in Gasprom for one year?
(5) (b) Find the probability that the annual return % on Gasprom shares will exceed the
annual return % on the UES shares.
(3) (c) Anatoly Chubais, the CEO of the UES, claims that there is a 30% chance that next
year the return on the UES shares will be more than R%. Find R.
2 Qu. #4. An unnamed government official claims that a Canadian taxpayer between 19
and 65 year old should expect to pay on average $20K ($20,000) in federal taxes in 2007
tax year. Assume that federal tax liabilities for Canadians are normally distributed
(6) (a) You have concerns about his/her estimates of the average tax liability – you think
it should be higher than $20K. You have randomly selected 10 people and computed their
federal tax liabilities as follows:
$28K $29K $27K $28K $25K $35K $24K $28K $19K $38K
Does this data indicate that the official’s estimation of the mean is too low? State your
reason clearly. (Hint: you may want to find a probability that any sample of size 10 will
result in a sample mean that is equal to or higher than the sample mean of your sample.)
(3) (b) What is the probability that the average tax payment of a randomly selected group
of 60 taxpayers is less than $18K if the standard deviation of the federal tax payments of
19-65 year old Canadian taxpayers is $8K.
(1) (c) What will be the effect on your answer to question (b) if the federal tax liabilities
were not normally distributed? State your reason clearly.
Qu. #5 (10 Marks)
A power-drink manufacturer fills large 750 mL bottles with the power-drink. To test if
the filling process is under control or not, the quality control department took 12 samples
of 5 observations each and recorded the actual amount of drink in the bottles. Chart#1 is
the resulting Xbar Chart based on the range, ‘R’ and Chart#3 is the resulting Xbar Chart
based on the standard deviation, ‘s’. The Table Values of Control Chart Constants are
given at the end of this Question. When asked, the UCL and LCL values must be
calculated by using appropriate values from this table.
XBar Chart based on R
l 750.5 _