CIMA - C3 Fundamentals Of Business Mathematics
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330 Question bank
30 Identify the sampling methods that require a sampling frame by putting a tick (9) in the relevant box.
Sampling method Sampling frame required (
9)
Random
Stratified
Quota
Systematic
31 In a histogram, one class is two thirds the width of the other classes.
If the score in that class is 20, the correct height to plot on the histogram is
A 13.33
B 21.00
C 30.00
D 33.33
32 A histogram uses a set of bars to represent a grouped frequency table. To be correctly presented, the
histogram must show the relationship of the rectangles to the frequencies by reference to the
A Diagonal of each bar
B Area of each bar
C Width of each bar
D Height of each bar
33 The graph below is an ogive showing the value of invoices selected in a sample.
Which of the following statements is true?
A There are 100 sales with values of $60
B There are more than 100 sales with values of $60 or more
C There are 100 sales with values of less than $60
D There are more than 100 sales with values of $60 or more and there are 100 sales with values of
less than $60
Question bank 331
The following data relate to questions 34-36
The distribution of average weekly wages paid to direct labour employees at the factory of Parrots Co is as follows.
Weekly average wage Number of employees Frequency density Cumulative frequency
$
51 and < 61 13 A
61 and < 66 12 B
66 and < 71 16 C
71 and < 76 21 E
76 and < 81 25 F
81 and < 86 20
86 and < 91 14
91 and < 101 9 D G
34 Using a standard interval size of $5, calculate the frequency densities corresponding to the letters A, B, C
and D.
A =
B =
C =
D =
35 Illustrate the data given above by means of a histogram.
332 Question bank
36 Calculate cumulative frequencies corresponding to the letters E, F and G as shown in the table above.
E =
F =
G =
37 Illustrate the data given above by means of an ogive.
38 Over a period, a firm made purchases of $800, $1,000, $1,100 and $1,200 on items, the unit cost of which
were $5.00, $6.25, $5.50 and $6.00 respectively.
To the nearest penny, the mean price paid per item was
A $5.69
B $5.70
C $5.71
D $5.72
39 The following scores are observed for the times taken to complete a task, in minutes.
24, 68, 28, 30, 42, 48, 18, 34, 22, 16
The median score is
A 26
B 28
C 29
D 32
Question bank 333
40 The arithmetic mean of nineteen numbers is 10. When a twentieth number, x, is added the overall mean
becomes 11. What is the value of x?
A 15
B 20
C 25
D 30
41 The sales of colour televisions on each of 40 days was as follows.
Daily sales Frequency Midpoint
f x fx
> 0 ≤ 3
8
> 3 ≤ 6
16
> 6 ≤ 9
12
> 9 ≤ 12
4
40
Fill in the gaps in the table above.
The variables in the table are discrete/continuous.
The arithmetic mean of the data = ……………………….
42 Journey times to work of employees of a company were as follows.
Time
No of employees
Minutes
less than 10 14
10 but " " 20 26
20 " " " 30 64
30 " " " 40 46
40 " " " 50 28
50 " " " 60 16
60 " " " 80 8
80 " " " 100 4
Required:
Calculate the mean journey time, giving your answer correct to two correct decimal places.
minutes
43 Given that Σ f = 23, Σ fx = 79 and Σ fx
2
= 1,161, calculate the standard deviation (to two decimal places)
44 A statistician wishes to compare the dispersion of four frequency distributions. Data for the distributions
are as follows:
Distribution Mean Standard deviation
1 $140 $33
2 $25,104 $6,290
3 77 kg 27 kg
4 154 miles 32 miles
334 Question bank
The relative dispersion of the distributions is to be measured using the coefficient of variation. Which
frequency distribution has the largest coefficient of variation?
A Distribution 1
B Distribution 2
C Distribution 3
D Distribution 4
45 What is the variance of the five numbers, 4, 6, 8, 12, 15?
A 8.9
B 9.0
C 16
D 80
46 An index of machine prices has year 1 as the base year, with an index number of 100. By the end of year 9
the index had risen to 180 and by the end of year 14 it had risen by another 18 points.
What was the percentage increase in machine prices between years 9 and 14?
A 2%
B 9%
C 10%
D 18%
47 The mean weekly take-home pay of the employees of Staples and a price index for the 11 years from 20X0
to 20Y0 are as follows.
Year Weekly wage Price index (20X0 = 100)
$
20X0 150 100
20X1 161 103
20X2 168 106
20X3 179 108
20X4 185 109
20X5 191 112
20X6 197 114
20X7 203 116
20X8 207 118
20X9 213 121
20Y0 231 123
Question bank 335
Complete the following table in order to construct a time series of real wages for 20X0 to 20Y0 using a
price index with 20X6 as the base year.
Year Index Real wage
$
20X0
20X1
20X2
20X3
20X4
20X5
20X6
20X7
20X8
20X9
20Y0
48 Stuart Co wishes to construct a price index for three commodities, A, B and C.
20X0 Prices relative to 20X0 (%)
Quantities 20X1 20X2
A 5,000 100 110
B 6,000 108 115
C 3,000 90 100
Required:
(a) Calculate the weighted average of price relative index for 20X1 with base 20X0 using 20X0 quantities
as weights. Give your answer to one decimal place.
(b) Calculate the weighted average of price relative index for 20X2 with base 20X0 using 20X0 quantities
as weights. Give your answer to one decimal place.
49 A distributor has recorded the following demand for an item of inventory over the last 200 days.
Daily demand Number of days
Units
50 27
51 35
52 38
53 42
54 57
If these data are representative of the normal pattern of sales, what is the probability of a daily demand of 53
units?
A 17.5%
B 19.5%
C 21.0%
D 28.5%
336 Question bank
50 Next year, sales may rise, fall or remain the same as this year, with the following respective probabilities:
0.61, 0.17 and 0.22.
The probability of sales remaining the same or rising is
A 0.13
B 0.17
C 0.70
D 0.83
51 A salesman has three small areas to cover, areas x, y and z. He never sells more than one item per day and
the probabilities of making a sale when he visits each area are as follows.
Area Probability
x 0.40
y 0.35
z 0.25
He visits only one area each day. He visits area x twice as often as he visits areas y and z.
Calculate the EV of probability of a sale in each of the areas x, y and z and the probabilities of visiting each
of the areas.
Probability of visiting area x =
Probability of visiting area y =
Probability of visiting area z =
EV of probability of a sale in area x =
EV of probability of a sale in area y =
EV of probability of a sale in area z =
Select your answers from the list below.
0.0625
0.0875
0.20
0.25
0.25
0.50
52 Calculate the following probabilities, giving all answers correct to 3 significant figures.
(a) Drawing two aces from a pack of 52 playing cards in two successive draws (with and without
replacement).
With replacement
Without replacement
Question bank 337
(b) Drawing the ace of hearts and the ace of spades in that order (assuming replacement).
(c) It is assumed that home, car and television ownership are independent. Selecting from a list of
respondents to a questionnaire used in a sample survey it was found that 50% owned their own
homes, 60% owned a car and 90% had a television set. The probability that a respondent who
owned:
(i) his home and a car =
(ii) all three of the above assets =
(iii) none of the above assets =
(d) Suppose that 50% of respondents owned their own homes and 60% owned a car. In addition, it was
found that the percentage of home owners who owned a car was 80%.
(i) Find the percentage of car owners amongst those respondents who do not own their own
home.
(ii) If a car owner is selected at random, find the probability that he/she is also a home owner.
53 A business is deciding whether to buy a new machine. The machine may contribute extra profits of $15,000
or $19,000 or a loss of $1,000, with associated probabilities of 0.2, 0.6 and 0.1 respectively.
What is the expected profit?
A $35,000
B $14,300
C $19,000
D $11,667
54 What is illustrated in this diagram?
A A pie chart
B A Venn diagram illustrating two mutually exclusive outcomes
C An ogive
D A Venn diagram illustrating complementary outcomes
A B
338 Question bank
55 Which of the following rules of probability is used when we wish to determine the probability of one event
or another occurring and the two events are not mutually exclusive?
A P(A) + P(B)
B P(A) x P(B)
C P(A)/P(B)
D P(A) + P(B) – P(A and B)
56 Which of the following is/are limitations of using expected values when evaluating decisions?
I Expected values do not consider attitudes to risk
II All the profits and probabilities need to be estimated
III The time value of money may not be taken into account
IV They do not allow for changes in circumstances
A I and IV
B II and IV
C I, II and III
D II, III and IV
57 A quality inspector examines 25, 50 and 75 items from three production lines, red, yellow and green
respectively. Records of previous inspections show that the rate of faulty items on each production line is
Red Yellow Green
4% 12% 20%
Complete the following table by filling in the values represented by letters.
Red Yellow Green Total
Good C
Faulty A B
Total 25 50 75 150
A =
B =
C =
58 The weights of elephants are normally distributed. The mean weight is 5,200 kg and the probability of an
elephant weighing over 6,000 kg is 0.0314. What is the standard deviation of the weights of elephants?
A 186 kg
B 215 kg
C 372 kg
D 430 kg
59 A normal distribution has a mean of 60 and a standard deviation of 3.8.
The probability of a score of 56 or less is
A 85%
B 50%
C 35%
D 15%
Question bank 339
60 In a normal distribution with a standard deviation of 90, 28.23% of the population lies between the mean
and 900. The mean is
A 860
B 850
C 840
D 830
61 A normal distribution has a mean of 200 and a variance of 1,600.
Approximately 20% of the population is above which of the following values?
A 234
B 240
C 251
D 278
62 Consider the following normal distribution.
Which area represents the probability that:
(a) x < 120
(b) x is between 120 and 150
(c) x > 150
(d) x > 120
63 A company produces batteries whose lifetimes are normally distributed with a mean of 100 hours. It is
known that 96% of the batteries last at least 40 hours. Throughout this question all answers should be
given correct to one decimal place.
(a) If P(z > a) = 0.96, use normal distribution tables to find the value of 'a'.
a =
(b) Estimate the standard deviation lifetime.
(c) Calculate the percentage of batteries that will last less than 57 hours.