Download Multiple choice test from Spring 1998

BUSINESS STATISTICS
MULTIPLE CHOICE TEST
SPRING 1998
SUBJECT CODE:
QBM117
DATE:
7 October 1998
TIME ALLOWED:
90 minutes only
CLOSED/OPEN BOOK:
Open book to Selvanathan text or Anderson 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 that
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 1998
Page 1 of 6
Use the information given below to answer questions 1. to 4.
Suppose you are a budding entrepreneur. The start-up costs, in thousands of dollars,
for Entrepreneur Magazine’s 25 most popular franchises are summarised below.
800.000
600.000
400.000
Outer Fence
Whisker
200.000
0.000
50
150
250
350
450
550
650
3rd Quartile
M edian
Whisker 1st Quartile
-200.000
Inner Fence
-400.000
Outer Fence
-600.000
1.
The franchise Hardees has the highest start-up costs. What is the approximate
start-up cost for a Hardees restaurant?
A.
B.
C.
D.
E.
2.
The shape of this distribution of start-up costs is
A.
B.
C.
D.
E.
3.
$660
$600
$300 000
$660 000
$600 000
approximately normal.
positively skewed.
negatively skewed.
uniform.
skewed to the left.
It was reported that for these 25 franchises, the typical start-up cost was
$160 700. Which measure of centre is this value most likely to represent?
A.
B.
C.
D.
E.
mean
median
mode
the 50th percentile
standard deviation
QBM117 Multiple Choice Test – Spring 1998
Page 2 of 6
Outliers
Cost ($000's)
Inner Fence
Interquartile
Range
16
14
12
10
8
6
4
2
0
Outliers
No. franchises
Start-up costs for 25 of the most popular
franchises
4.
What does the value marked with an arrow on the boxplot correspond to?
A.
B.
C.
D.
E.
5.
the 75th percentile
the largest observation
an outlier
the 25th percentile
the largest value that is not considered a potential outlier
The mean and standard deviation for the following sample of 10 numbers
12 15 20 14 15 12 20 19 26 29
A.
B.
C.
D.
E.
6.
A simple random sample of size 8 is selected from a population of 40. The
probability that a particular member is the first one selected is
A.
B.
C.
D.
E.
7.
0.025
0.125
0.2
0
none of the above
Two events A and B are independent. If P(A) = 0.5 and P(B) = 0.3
then P(B|A) is
A.
B.
C.
D.
E.
8.
are 18.2 and 5.47 respectively.
are 18.2 and 29.96 respectively.
are 18.2 and 5.77 respectively.
are 18.2 and 33.29 respectively.
are none of the above values.
0.15
0.30
0.67
0.50
unable to be determined due to insufficient information.
Which of the following is an example of a continuous random variable?
A.
B.
C.
D.
E.
The weight of a packet of lollies.
The number of lollies in a bag.
The number of phone calls received by a switchboard in an hour.
The number of workers absent today.
The number of questions answered correctly on a multiple choice test.
QBM117 Multiple Choice Test – Spring 1998
Page 3 of 6
9.
A market researcher is asked to visit 15 homes in a given area between 7:30
and 9:30 one evening. Previous calls suggest that there will be someone at
home in 90% of homes. Find the probability that the researcher will find
someone at home in exactly ten homes.
A.
B.
C.
D.
E.
10.
A test has been conducted to see if a road intersection should be improved.
During this test it was found that cars arrive randomly and independently at
the intersection at an average rate of 15 cars every half an hour. What is the
probability that more than five cars will arrive during a ten minute period?
A.
B.
C.
D.
E.
11.
0.013
0.011
0.987
0.056
0.349
0.560
0.997
0.762
0.616
0.384
Given Z is the standard normal random variable, find the probability that
P(1.5 < Z < 2.5)
A.
B.
C.
D.
E.
0.9270
0.0606
0.9394
0.9938
0.1267
Use the following information to answer questions 12. and 13.
A fast-food restaurant finds that the number of meals that it serves in a week is
normally distributed with a mean of 6000 and a standard deviation of 600 meals.
12.
What is the probability that in a given week the number of meals served will
be less than 5000?
A.
B.
C.
D.
E.
13.
0.0475
0.4525
0.5475
0.0485
0.4515
There is a 90% chance that the number of meals served in the restaurant will
exceed
A.
B.
C.
D.
E.
6768
5850
5940
5232
5226
QBM117 Multiple Choice Test – Spring 1998
Page 4 of 6
14.
The standard error for the sample mean gives a measure of
A.
B.
C.
D.
E.
15.
A machine is set to produce bolts with a mean length of 3.5cm. A quality
control inspector takes a random sample of 50 bolts and calculates a mean bolt
length of 3.7cm and a standard deviation of 0.8cm. Find the probability of
getting a sample mean that size or larger if the machine is set correctly.
A.
B.
C.
D.
E.
16.
0.4616
0.0987
0.4013
0.0384
0.9616
Timball Corporation employs 5600 workers. 60% of the workers are male.
25% of the workers earn more than $30 000 a year. 15% of the workers are
male and earn more than $30 000 per year. If an employee earns more than
$30 000 a year, what is the probability that the employee is female?
A.
B.
C.
D.
E.
17.
the dispersion of values in the sample.
the dispersion of values in the population.
how far away a particular sample mean is from the population mean.
the dispersion of the values of the sample mean for all possible
samples.
the variability of the data.
0.15
0.45
0.10
0.30
0.40
A sample of 24 observations is taken from a large population. The sampling
distribution of the sample mean is
A.
B.
C.
D.
E.
approximately normal because the sample means are always normally
distributed.
approximately normal because the sample size is large.
approximately normal because the sample size is small.
approximately normal because of the central limit theorem..
normal if the population is normally distributed.
QBM117 Multiple Choice Test – Spring 1998
Page 5 of 6
18.
For a continuous uniform distribution with limits of 10 and 20, the range
defined by one standard deviation either side of the mean is
A.
B.
C.
D.
E.
19.
The reason why the standard deviation of a distribution is more easily
interpreted than the variance is that
A.
B.
C.
D.
E.
20.
12.11 to 17.89
5.77 to 11.55
4.22 to 25.78
9.22 to 20.78
6.67 to 23.33
it is a measure of average deviation.
it is expressed in the same units as the data.
it takes into account every data value.
it is standardised
it takes the mean into account.
A bag contains 1 yellow and four red balls. A ball is drawn at random from the
bag and the colour recorded. The ball is then replaced and the bag shaken.
This is repeated three times more. How likely is it that we observe 4 yellow
balls?
A.
B.
C.
D.
E.
0.8
0.2
0.16
0.64
0.0016
QBM117 Multiple Choice Test – Spring 1998
Page 6 of 6