Use the information below to answer Question 12 and Question 13. People arrive at a checkout in a supermarket randomly, and at a constant mean rate of 0.5 per minute. Assume the arrival times follow a Poisson distribution. Find the probability that exactly 3 people arrive at the checkout during a 5-minute period. A. 0.5438 B. 0.4562 C. 0.2138 D. 0.7576 Question 13 Find the probability that at least 2 people will arrive at the checkout in a 2-minute interval.
Question 12
Use the information below to answer Question 12 and Question 13.
People arrive at a checkout in a supermarket randomly, and at a constant mean rate of 0.5 per minute.
Assume the arrival times follow a Poisson distribution. Find the probability that exactly 3 people arrive at
the checkout during a 5-minute period.
A. 0.5438
B. 0.4562
C. 0.2138
D. 0.7576
Question 13
Find the probability that at least 2 people will arrive at the checkout in a 2-minute interval.
A. 0.1839
B. 0.2642
C. 0.7358
D. 0.0803
Question 14
The duration of a lunch break for one employee at a manufacturing company follows a
distribution
lunch break lasts for more than 52 minutes is 0.25. Find the value of µ.
A. 55.37
B. 46.25
C. 57.75
D. 48.63
Question 15
It is believed that 20% of school teachers in Gqeberha own a car. 16 teachers from Gqeberha
are chosen at random. Find the probability that the number of those teachers who own a car
is at least 2 and at most 4.
A. 0.2001
B. 0.2111
C. 0.2463
D. 0.6575
Question 16
Use the following information to answer Question 16 and Question 17.
A bag has 4 yellow balls and 6 red balls only. One ball is chosen at random and not replaced. A second
ball is then chosen at random.
Find the probability that both balls are yellow.
A. 2/15
B. 4/25
C. 2/5
D. 11/15
Question 17
Find the probability that both balls have the same colour.
A. 2/15
B. 1/6
C. 3/10
D. 7/15
Question 18
At a local club, the ages of the members and the times they took to run a 10 km race are
recorded. For a random sample of 25 club members aged between 27 and 60, their ages
(x years) and times (y minutes) produce the following regression line.
y = 0.83x + 41.28
Four new members join the club. Their respective ages (in years) are 26, 18, 22, and 28. When the
respective race times for the 4 new members are estimated, which one of these estimated race times
is the most reliable?
A. 62.86 minutes
B. 56.22 minutes
C. 59.54 minutes
D. 64.52 minutes
Question 19
The data of the number of ‘centuries’ i.e. a scores of 100 runs or more, scored by players at a
cricket club during a season are given in the following table.
Number of centuries Number of players
0 4
1 k
2 3
3 2
4 3
8 1
Given that the mean number of centuries scored per player is 1.95, find the value of k.
A. 7
B. 3
C. 4
D. 1
Question 20
The asking prices (in Rands) and the actual selling prices (in Rands), after bargaining, of 8
commodities are given below.
Commodity A B C D E F G H
Asking price, x 150 350 400 750 100 650 600 250
Selling price, y 120 200 400 550 80 450 350 200
Find the
A. 0.8224
B. 0.3722
C. 0.9438
D. 0.5318
Question 21
Use the following information to answer Question 21 and Question 22.
The prices and consumptions of basic goods in years 2010 and 2020 are given in the following table.
2010 2020
Unit Price
(Rands)
Quantities (kg) Unit Price
(Rands)
Quantities (kg)
Flour 15 62 26 78
Sugar 12 15 19 22
Maize meal 14 80 15 85
Evaluate the Paasche Price index for 2020 using 2010 as the base year for the above data.
A. 117.7
B. 120.1
C. 138.9
D. 141.8
Question 22
Evaluate the Laspeyres Quantity index for 2020 using 2010 as the base year for the above data.
A. 117.7
B. 120.1
C. 138.9
D. 141.8
Question 23
Two six-sided fair dice, one red and one white, each with faces numbered 1, 2, 3, 4, 5 and 6 are
thrown.
The following are some of the possible events.
Event 2: an even number is obtained on the white die
Event 3: an odd number is obtained on the white die
Event 4: a 4 is obtained on the white die
Which of the following events are mutually exclusive?
A. 1 and 3
B. 2 and 3
C. 2 and 4
D. 1 and 4
Question 24
A poultry business project requires an initial investment of R75 000. The business generates the
following incomes at the end of the given times.
6 months : R20000
12 months : R25000
18 months : R40000
The expected return on this project is 10% per annum. Find the net present value of this project.
A. -1251.23
B. 10000
C. 1467.89
D. -1780.11
Question 25
The following are pairs of independent variables and their corresponding dependent variables.
In which of these pairs of variables should the independent variable be interchanged with its dependent
variable?
Independent variable (x) Dependent variable (y)
A. Daily temperature Electricity consumption
B. Annual salary Number of vacations taken
C. Number of exams passed Amount of time spent studying
D. Alcohol consumption by drivers Number of accidents by those drivers
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