Download Use the information given below to answer questions 1

BUSINESS STATISTICS
MULTIPLE CHOICE TEST
SPRING 2001
SUBJECT CODE:
QBM117
DATE:
3 October 2001
TIME ALLOWED:
90 minutes only
CLOSED/OPEN BOOK:
Open book to Selvanathan text.
VALUE:
10% of the total assessment
INSTRUCTIONS
1. Enter your name and student number in the space provided on the answer sheet as
directed by the lecturer. Use a 2B pencil only.
2. Answer all 20 questions, each question has equal value. Marks are not deducted
for incorrect responses.
3. Each question has five responses A to E. On the answer sheet colour the response
that best answers the question. If your answer differs from all responses provided,
select that response that best approximates your answer.
4. Make heavy marks that fill the circle completely.
5. Erase cleanly any answers you may wish to change.
6. When you have completed the exam, hand in the answer sheet only.
7. Calculators are permitted
QBM117 Multiple Choice Test – Spring 2001
Page 1 of 6
Use the following information to answer question 1. and 2.
The following data represent the number of colour television sets manufactured each
day at a given factory, for a random sample of 15 days.
15
20
1.
14
34
12
25
22
40
23
41
25
the mean = 23 and the median = 22
the mean = 23.7 and there is no mode;
the range = 29 and the median = 22
the range = 29 and the mean = 23
the median = 20 and the mean = 23.7
The coefficient of variation is
A.
B.
C.
D.
E.
3.
19
17
Which of the following statements about the descriptive statistics for these
data are correct?
A.
B.
C.
D.
E.
2.
16
32
0.3
0.38
0.39
8.9
79.6
The boxplot following shows the distribution of student marks on a mid
session test where a mark of 50% or above is considered a pass.
BoxPlot
0
20
40
60
80
100
120
marks (%)
Choose the statement which correctly describes the performance of students
on this test.
A.
B.
C.
D.
E.
All the students passed the test.
50% of the students failed the test.
The median mark on the test was 60%
More than 75% of the students passed the test.
25% of students scored a mark of more than 80%.
QBM117 Multiple Choice Test – Spring 2001
Page 2 of 6
4.
Which of the following is an example of a discrete random variable?
A.
B.
C.
D.
E.
5.
The time a person waits in line at the supermarket.
The weight of a car.
The number of customers that enter a store daily.
The time it takes a worker to inspect a machine.
All of the above are examples of discrete random variables.
Let X be a random variable with the following probability distribution:
x
p (x)
0
0.1
1
0.3
2
0.4
3
0.2
The expected value and variance of this distribution would be
A.
B.
C.
D.
E.
6.
V ( X )  3.7
V ( X )  3.7
V ( X )  1.45
V ( X )  0.09
V ( X )  0.81
0.875
0.125
0.500
0.375
0.250
If P( A and B)  0.09 , P( A)  0.4 and P( B)  0.2 , find the probability of A
given that B has occurred.
A.
B.
C.
D.
E.
8.
and
and
and
and
and
A couple plans to have three children. Assume that the probability of having
a boy is 0.5. What is the probability of having at least one girl?
A.
B.
C.
D.
E.
7.
E ( X )  1.5
E ( X )  1.7
E ( X )  1.5
E ( X )  1.5
E ( X )  1.7
0.225
0.018
0.036
0.450
0.080
What type of scale is the measurement of the salaries of lecturers?
A.
B.
C.
D.
E.
a nominal scale
a discrete scale
a ratio scale
an ordinal scale
an interval scale
QBM117 Multiple Choice Test – Spring 2001
Page 3 of 6
Use the information following to answer questions 9. and 10.
A used car company determined that 30% of customers made a complaint about the
car, within one month of purchase.
9.
What is the probability that out of 10 randomly selected customers, only one
made a complaint within one month of purchase?
A.
B.
C.
D.
E.
10.
What is the probability that out of 10 randomly selected customers, more than
three made a complaint within one month of purchase?
A.
B.
C.
D.
E.
11.
0.251
0.060
0.809
0.242
0.980
If Z is the standard normal random variable, then P( Z  2.32) is
A.
B.
C.
D.
E.
13.
0.850
0.617
0.350
0.267
0.650
A bank officer finds that he serves an average of 1.4 customers every 5
minutes. If the customers arrive randomly and independently, what is the
probability that in the next 5 minutes, the bank officer serves exactly two
customers?
A.
B.
C.
D.
E.
12.
0.012
0.028
0.149
0.121
0.234
0.9898
0.4898
0.9893
0.0102
0.0002
If Z is the standard normal random variable, then P(0.3  Z  2.4) is
A.
B.
C.
D.
E.
0.6097
0.3739
0.3903
0.5972
0.3612
QBM117 Multiple Choice Test – Spring 2001
Page 4 of 6
Use the following information to answer questions 14. and 15.
Models of the pricing of stock options make the assumption of a normal distribution.
An analyst believes the price of a particular stock option is a normally distributed
random variable with mean $8.95 and variance 4.
14.
Find the probability that this particular stock option exceeds $11.00.
A.
B.
C.
D.
E.
15.
The analyst would like to determine the value a, such that there is a 90%
chance that the price of the option would be greater than this value. Find a.
A.
B.
C.
D.
E.
16.
$11.51
$8.45
$9.45
$8.75
$6.39
Consider a population whose distribution is non-normal with  = 0.5 and
 = 10.2. Assume the following sample results were obtained: n = 40,
X  12.5 . Under these circumstances, the distribution of the sample mean has
the following properties:
A.
B.
C.
D.
E.
17.
0.3485
0.0968
0.1515
0.1915
0.3085
approximately normal, mean = 10.2, standard deviation = 0.5.
non-normal, mean = 12.5, standard deviation = 0.08.
approximately normal, mean = 10.2, standard deviation = 0.08.
approximately normal, mean = 12.5, standard deviation = 0.08.
non-normal, mean = 10.2, standard deviation = 0.08.
The two events A and B are independent with P( A)  0.2 and P( B)  0.35 .
Find P( A | B)
A.
B.
C.
D.
E.
0.2
0
0.07
0.55
It is not possible to find P( A | B) due to insufficient information.
QBM117 Multiple Choice Test – Spring 2001
Page 5 of 6
18.
A pie chart is most useful for describing
A.
B.
C.
D.
E.
19.
qualitative data and relative frequencies.
quantitative data and frequencies.
quantitative data and relative frequencies.
qualitative data and frequencies.
qualitative data and cumulative frequencies.
Consider the following data on the number of students who either passed or
failed a statistics exam.
Men
Women
Fail
28
10
Pass
272
190
Given that a man has been randomly selected, the probability that he failed the
exam is
A.
B.
C.
D.
E.
20.
0.737
0.093
0.907
0.056
28
For a continuous uniform distribution with limits of 10 and 15, the range
defined by two standard deviations either side of the mean is
A.
B.
C.
D.
E.
8.3 to 16.7
9.6 to 15.4
7.1 to 12.9
10.0 to 15.0
11.1 to 13.9
QBM117 Multiple Choice Test – Spring 2001
Page 6 of 6