ACCN 102 QUESTION BANK 2024
QUESTION
(a) State the data measurement scales used for each of the following variables:
i. Product Price
ii. Age
iii. Number of defects
iv. Temperature
v. Gender
vi. Highest Educational Certificate (4 Marks)
(b) Outline three branches of statistics (6 Marks)
c). What are the benefits of statistics to business (8 Marks)
d). Briefly explain sampling techniques available (10 Marks)
e) Differentiate continuous from discrete data giving examples (4 Marks)
QUESTION
The following are the marks obtained by ten students in their ACCN 102 Exam:
84 76 90 92 65 56 46 45 67 87
(a) Determine
i. Average exam mark (1 Mark)
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ii. Standard deviation (3 Marks)
iii. Median mark (2 Marks)
iv. Kurtosis (2 Mark)
v. Skewness and comment (4 Marks)
(b) Present the ACCN 102 Exam data set on a five-number diagram (3 Marks)
(c) Outline steps you would take to obtain descriptive statistics output in Microsoft Excel
(4 Marks)
d). A courier company recorded 30 delivery times (in minutes) to deliver parcels to their
clients from its depot. The data is summarised in the numeric frequency distribution
and ogive as shown in table below.
Time Frequency Cumulative
10 - <20 3 3
20 - <30 5 8
30 - <40 9 17
40 - <50 7 24
50 - <60 6 30
Required
i. Median delivery time
ii. Standard deviation
iii. Mean delivery time
iv. Mode
v. Use Ogive graph to determine median, first quartile (25 percentile) and third quartile
(75 percentile).
QUESTION
The following relates to test 1 and 2 scores data and output from excel
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Required
(a) Calculate the correlation coefficient to confirm the above result (Show all your
working) (5 Marks)
(b) Interpret the correlation between test 1 and test 2 scores. (4 Marks)
(c) Determine the covariance between Test 1 and Test 2 scores
QUESTION
(a) Given the following sets of numbers,
A=(1,2,3,4,5)
B=(4,5,6,7,8,9)
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Determine P(A/B) (3 Marks)
(b) Confirm your answer in (a) above using Baye’s Theorem (2 Marks)
(c) A multiple-choice test contains twenty (20) questions with possible answers A, B,
C and D. Only one answer is correct for each question.
i. Find the probability that a student guessing will answer exactly six (6)
questions correct out of the twenty (20) attempted. (4 Marks)
ii. Determine the mean and standard deviation of the distribution. (3 Marks)
(d) Dinner Inn (Pvt) Ltd receives on average 6 calls per hour enquiring about food.
i. Calculate the probability that Dinner Inn will receive exactly 4 calls in one
hour (2 Marks)
ii. Find the probability that the business will receive at most 3 calls in one
hour (4 Marks)
iii. Determine the probability that the business will receive at least 2 calls in
two hours. (6 marks)
(e) Test scores of a statistics class with 800 students are normally distributed with
mean of 75 and standard deviation of 7.
Compute the following:
i. Percentage of the class with test scores between 68 and 82 (2 Marks)
ii. Number of students with test scores between 61 and 89 (3 Marks)
iii. Probability that a student chosen at random has a score between 57 and 75
(3 Marks)
iv. Number of students with scores greater or equal to 96. (4 Marks)
QUESTION
A survey of a random sample of 300 grocery shoppers in PicknPay found that the mean value
of their grocery purchases was USD78. Assume that the population standard deviation of
grocery purchases was valued at USD21. [ z0.01/2 =+/-2.58, z0.05/2 =+/-1.96]
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Required
(a) Find the 95% confidence limits for the average value of a grocery purchase by all gro-
cery shoppers in PicknPay (5 Marks)
(b) Comment on your answer on (a) above (2 Marks)
QUESTION
DZ Steel Company manufactures and assembles desks and other office equipment The
weekly production of the Model A325 desk at the Kadoma Plant follows the normal
probability distribution with a mean of 200 and a population standard deviation of 16.
Recently, new production methods have been introduced and new employees hired. Using
50 weeks, the manager measured the average production to be 203.5. The CEO of
manufacturing would like to investigate whether there has been a change in the weekly
production of the Model A325 desk. [ z0.01/2 =+/-2.58, z0.05/2 =+/-1.96]
(a) State the null and alternative hypotheses (2 Marks)
(b) Test the hypothesis in (a) above at 1% significance level (8 Marks)
QUESTION
The sales manager gathered the following information on the number of sales calls made
and the number of copiers sold for a random sample of 10 sales representatives. Use the
least squares method to determine a linear equation to express the relationship between
the two variables.
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(a) Present the data above on a scatter plot (5 Marks)
(b) Determine:
i. Alpha, (2 Marks)
ii. Beta of the regression equation (5 Marks)
(c) Write down the regression equation (1 Mark)
(d) Calculate the expected number of copiers sold by a representative who made 20 calls.
(2 Marks)
QUESTION
The following table shows data on 300 employees of a glass manufacturing company,
cross-classified on the basis of age and department:
Age Department Total
Production Sales Administration
Age Departments Total
Production Sales Administration
<30 60 25 18 103
30-50 70 29 25 124
>50 30 8 35 73
Total 160 62 78 300
(a) An employee is selected at random from this company. Calculate the probability
that the employee is:
(i) under 30 years of age
(ii) a production worker
(iii) a sales person and between 30 and 50 years of age
(iv) over 50, given that he or she is in administration
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(v) a production worker or under 30 years, or both.
(b) Are the two events ‘age’ and ‘department’ mutually exclusive? Justify your
answer.
(c) Are age and department statistically independent? Justify your answer.
(d) State the probability type and probability rule, if appropriate, used in each of
(a)(i)–(v).
QUESTION
Explain any two differences among descriptive statistics, inferential statistics and statistical
modelling. [9 Marks]
a. With reference to practical examples explain the meaning of the four measurement
scales. [4
Marks]
b. Explain any two differences between a sample and a population. [4 Marks]
c. Explain any four advantages of sampling. [8 Marks]
d. Outline the any 3 advantages of statistics in a business. [6 Marks]
e. The marks of students from a test have been found to follow a normal probability dis-
tribution with a mean score of 60% and a standard deviation of 25%.
i. Compute the probability of scoring less than 50%. [3 Marks]
ii. In a class of 20 students, how many students would score between 50% and
75%.
[4 Marks]
f. In a production flow process, defects occur at the rate of 5 per hour.
i. Compute the probability of observing 7 defects in the next hour. [3 Marks]
ii. Compute the mean and standard deviation of this Poisson distribution. [2
Marks]
iii. Compute the standard deviation of this Poisson distribution. [2 Marks]
QUESTION
You are comparing the price and quantities of two products, Item A and Item B between
2009 and 2011. The prices and quantities are summarised in the table below.
Quantity Unit Price
2009 2011 2009 2011
Item A 1500 1800 7.5 7.75
Item B 2 1 630 1500
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Required
a. Compute price relatives for each item in 2011 using 2009 as the base period. [3
Marks]
b. Compute an unweighted aggregate price index for the two items in 2011 using 2009
as the base period. [3 Marks]
c. Compute a weighted aggregate price index for the two items using the Laspeyres
method. [4 Marks]
d. Compute a weighted aggregate price index for the two items using the Paasche
method. [4
Marks]
e. Explain the importance of price indices. [6 Marks]
QUESTION
The following table reports the percentage of stocks in a portfolio for nine quarters from 2010
to 2012.
Quarter Year Stock %
1 2010 29.8
2 2010 31
3 2010 29.9
4 2010 30.1
1 2011 32.2
2 2011 31.5
3 2011 32
4 2011 31.9
1 2012 30
Required:
a. Construct a time series plot. [4 Marks]
b. Explain the type of pattern existing in the data. [2 Marks]
QUESTION
a. You are a manager for a tele-communications company. You have four subscription
packages, Package A to Package D. You want to evaluate the subscriptions by gender
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for a sample of 100 subscriptions. You are informed that 47% of the subscribers are
female. Package A has 15 males whilst Package C has 14 males. Package B has 10 fe-
males and 12 males. Package A constitute 33% of the sample whilst Package D con -
stitutes 22% of the sample.
Required:
i. If you were to select an individual at random, determine the probability of picking:
1. A female who subscribes to Package C. [2 Marks]
2. A male given that he subscribes to Package C. [2 Marks]
ii. If you were to select two individuals at random, determine the probability of picking:
1. A male and a female. [3 Marks]
2. A male or subscribes to Package C. [3 Marks]
QUESTION
a. Use the appropriate data visualisation methods to present the following data.
i. Data on rainfall patterns. [4 Marks]
Year 2005 2010 2015 2020
Rainfall (mm) 40 55 42 38
ii. Data on gender in a class. [3 marks]
Gender Male Female
Number 150 120
b. You are given the following data on scores in a performance assessment.
54 66 72 45
82 58 53 67
80 77 78 76
62 64 66 74
54 49 60 62
Required:
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i. Construct a stem and leaf plot for the data. [4 Marks]
K log N
ii. You have used the formula 2 > N∨K = to determine the number and found
log 2
it to be 5. Group the data into 5 classes. [2 Marks]
iii. Construct a Box and whisker (5-Number) plot on the grouped data and comment
on the distribution of the data. (Hint: compute Q1, Q2 and Q3 first) [7
Marks]
QUESTION
DZ is in the process of deciding whether to purchase a maintenance contract for its new
computer wheel alignment and balancing machine. The operations manager wants to enquire
whether maintenance expense is related to usage. The following information was collected on
weekly usage (hours) and annual maintenance expense (in thousands of dollars).
Week Weekly Usage (hours) Annual Maintenance Expense
($000)
1 13 17
2 10 22
3 20 30
4 28 37
5 32 47
6 17 30.5
7 24 32.5
8 31 39
9 40 51.5
10 38 40
Required:
a. Develop the estimated regression equation that relates annual maintenance expense to
weekly usage. [10 Marks]
QUESTION
Global Insurance has found that 20% (one in five) of all insurance policies are surrendered
(cashed in) before their maturity date. Assume that 10 policies are randomly selected from
the company’s policy database.
(a) Determine the probability that four of these 10 insurance policies will have been
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surrendered before their maturity date.
(b) Calculate the probability that no more than three of these 10 insurance policies will
have been surrendered before their maturity date.
(c) Determine the probability that at least two out of the 10 randomly selected policies will
be surrendered before their maturity date.
QUESTION
A telemarketing company that sells homeowner insurance has found that 15% of all calls
made to households lead to a sale of a homeowner insurance policy. Assume that each call is
independent of all other calls.
(a) Find the probability that no sales result from 12 calls.
(b) Determine the likelihood that fewer than three homeowner policies are sold in
15 calls.
QUESTION
A telephone helpline receives calls that can be described by the Poisson process. The average
rate at which calls come in is three calls per minute.
(a) Find the probability that the helpline will receive exactly five calls in a given minute.
(b) Find the standard deviation of the above distribution.
(c) What is the likelihood that the helpline will receive four or more calls in a given
minute?
(d) What chance is there that no calls will be received in five minutes?
QUESTION
The data in the table below shows the usage of a basket of three toiletry items in two-person
household in Mutoko for 2020 and 2024 respectively. The data was collected from
household surveys.
Toiletry Items Base Year (2020) Current Year (2024)
Unit Price (Po) Quantity (Qo) Unit Price (P1) Quantity (Q1)
Soap $1.95 37 $2.10 40
Deodorant $14.65 24 $15.95 18
Toothpaste $6.29 14 $6.74 16
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Using 2020 as base year, calculate:
i. Price Relatives for each item
ii. Laspeyres Price Index
iii. Paasches Price Index, and comment on your answers
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