CURTIN UNIVERSITY
BUSINESS STATISTICS 101
MID-SEMESTER-TEST
SECOND SEMESTER 2004
BENTLEY CAMPUS
FAMILY NAME:
GIVEN NAME:
STUDENT NUMBER:
TUTOR’S NAME:
TUTORIAL TIME AND ROOM:
Aids allowed: as on unit outline. Time allowed: 1+hour.
_____________________________________________________
Question 1
A population is known to be normally distributed with a mean
of 70 and a standard deviation of 10. What is the probability
that an individual will have a value between 75 and 90?
(1-mark)
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Question 2
A certain species of fish appears to range in weight from
about 10kg to about 26kg. How large a sample should be taken
to estimate their mean weight to an accuracy of 3 kg with 90%
confidence?
(1-mark)
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Question 3
The average number of cars sold at a used-car yard on 9 days
selected at random was 7 per day. If the standard deviation is
known to be 2.3, estimate the true mean daily sales with 99%
confidence.
(1-mark)
Question 4
A quality inspector believes that the actual mean weight of
‘200gram blocks of chocolate’ differs substantially from what
is stated on the label. She finds that a sample of 25 blocks
has an average weight of 195grams. The standard deviation of
all such blocks is known to be 10grams. Test her belief at the
5% level of significance.
(2-marks)
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Question 5
A machine operates to fill soft drink containers to an average
of 1050ml with a standard deviation of 20ml. At what quantity
should a guarantee be offered so that not more than 5% of
containers have less than the specified amount?
(2-marks)
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Question 6
If each student has 80% chance of passing this unit, what is
the probability that in a class of 15 students not less than 5
will fail?
(2-marks)
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Question 7
The average number of tellers attending to customers in a
particular bank is 4. How many tellers should be available if
the manager wants to ensure that at least 90% of customers
will be able to receive immediate service?
(2-marks)
Question 8
The table below shows the joint probabilities for gender and
the type of transport used:
Public Transport
Private Vehicle
Foot
Male
0.2
0.1
0.2
Female
0.0
0.3
0.2
a) What is the probability that a female will use a private
vehicle?
(1-mark)
b) Are ‘Female’ and ‘Public Transport’ mutually exclusive?
Why?
(1-mark)
c) Are ‘Male’ and ‘Foot’ independent? Why?
(1-mark)
d) What is the probability that a person is female or uses a
private vehicle?
(1-mark)
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Question 9
Attendances at 15 club meetings were as follows:
20 23 37 44 52 32 25 50 43 36 30 28 51 47 22
a) Find the mean.
(1-mark)
b) Find the standard deviation of this sample.
(1-mark)
c) Determine the mode.
(1-mark)
Question 10
Using the group limits 10.5-13.5, 13.5-16.5, 16.5-19.5, 19.522.5, 22.5-25.5 for the data below
12 14 15 15 16 17 17 18 18 18 19 20 21 21 22 25
a) Set up a suitable frequency table.
(1-mark)
b) Draw an Ogive
(1-mark)
END OF TEST