2023_sats_nov_paper1

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For Performance Measurement

ZIMBABWE SCHOOL EXAMINATIONS COUNCIL

General Certificate of Education Advanced Level

STATISTICS . 6046/1
PAPER 1

NOVEMBER 2023 SESSION 3 hours

Additional materials:

Answer paper

Graph paper

List of Formulae MF 7
Scientific calculator [Non-programmable]
Mathematical Instruments

TIME 3 hours

INSTRUCTIONS TO CANDIDATES

Write your Name, Centre number and Candidate number in the spaces provided on the answer
paper/ answer booklet.

Answer all questions.

Ifa numerical answer cannot be given exactly and the accuracy required is not specified in
the question, then in the case of an angle it should be given to the nearest degree, and in other
cases it should be given correct to 2 significant figures.

INFORMATION FOR CANDIDATES

The number of marks is given in brackets [ ] at the end of each question or part question.

The total number of marks for this paper is 120.

The use of a non-programmable scientific calculator is expected, where appropriate.

You are reminded of the need for clear presentation in your answers.

This question paper consists of 6 printed pages and 2 blank pages.

Copyright: Zimbabwe School Examinations Council, N2023.

©ZIMSEC N2023 [Turn over

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2

1 (a) 6) Describe how direct observation can be used to collect data
for the annual rainfall pattern at a particular weather
station. [2]
(ii) _—_‘ State any one advantage and one disadvantage of using
direct observation as a method of data collection. [2]
2 (a) _ Define the terms

(i) Mutually Exclusive events
(ii) —_ Independent events [2]

(b) = Anelectronic display is equally likely to show any one of the digits
1, 2, 3 ....9. Determine the probability that

(i) it shows a prime number, [1]
(ii) _ it shows an odd number given that itisa prime number. [2]

8) The prices ($) of a pair of a certain type of male shoes in an informal
market of a particular country are as follows:

34.95 44.95 49.95 69.95

54.95 64.95 64.95 54.95

24.95 14.95 19:95 39.95

29.95 74.95 79.95

Calculate the mean and standard deviation for the sample. [5]
4 From a standard pack of 52 playing cards, 6 cards are chosen without

replacement. Find the probability that exactly 4 out of the 6 cards chosen

are spades. [5]
5 (a) Distinguish between a permutation and a combination. [2]

(b) A librarian has to arrange 9 books on the bookshelf of which four
are from the same author. Find the number of arrangements of the

books if
(i) there are no restrictions on the order of arrangement, [i]
(ii) books of the same author are to stay together. [2]

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6 (a) State Bayes theorem. [2]

(b) A manufacturer makes writing pens using two machines. His bigger
machine manufactures 75% of the pens and his smaller machine
manufactures the remaining 25%. From the bigger machine 5% of
the pens are defective and from the smaller machine 8% of the pens
are defective. A pen is selected at random.

Find the probability that the pen came from the bigger machine
given that it is defective. [3]

7 In a certain country the proportion of drivers for passenger vehicles who
pay a fine at a particular police road block for miscellaneous offences is
24%

If 15 drivers for passenger vehicles pass by the police road block, find the
probability that

@ exactly three pay a fine, [3]

(ii) three or more pay a fine. [3]
8 A boy is thinking of playing a game. To play the game he has to pay $4

and he will toss three fair coins. He will be awarded in dollars twice the

number of heads obtained.

(a) __ Find the boy’s expected win or loss in the game. [4]

(b) With regards to winning or losing would you advise him to play
the game? Justify your answer. [2]

9 The table below shows the marks obtained by 12 students in recent
Mathematics and Physics tests.

ek |?

Physics 5S 1 80

pli ven fe

%
(a) Calculate x and y. [2]
(b) Draw a scatter diagram to illustrate the marks in the two tests. [3]
(c) Draw a line of best, fit [2]
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4 10 (a) State conditions under which a normal distribution can be used as an approximation to the Binomial distribution. [3]

(b) —_Inaclass of 50 students, 20% of them enjoy basketball as their
favourite sport. Use a suitable approximation to find the probability
that more than 15 out of the 50 students enjoy basketball as their
favourite sport. [4]

11 The random variable X has probability distribution table given below.

(a) __ the value of k. [2]
(b) E(x) [2]
(c) Var(x) [3]
12 (a) Define a time series. [3]
(b) State the three types of variations in a time series. (4]

(c) State the number of 4-point moving averages that are there for the
following set of time series values.

20, 34, 40, 23, 27, 32 1]

13 A cement manufacturer claims that the newly introduced special type of
cement has a 0,95% success rate in producing strong walls.

A construction company buys the cement and uses it to build 20 houses
for their clients. After one year 16 of the clients said that their houses were
strong because of the cement.

(a) Test the cement manufacturer’s claims at 5% significance level. (5]

(b) Should the construction company recommend the cement to other
construction companies? [1]

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5 14 (a) The random variable X has a Bernoulli distribution with standard deviation =. Find the possible values of the expectation of X. [4]

(b) X ~ Geo (0,7)

Find the

() mode, [1]
(ii) mean of X, [2]
(iii) standard deviation of X. [2]

15 (a) State any two conditions necessary for a random variable to be
modelled using a Poisson distribution. [2]

(b) If X ~ Po(4,5)

(i) State the mean and standard deviation. [2]
(ii) ~~ Find P(X > 6). [2]
(ii) += If P(X < a) = 0,5321, find a [2]

16 The following table shows the results of a survey to find the average daily
time, in minutes, that a group of school children spent in an internet café.

[ TIME PER DAY (t minutes) FREQUENCY

0<t<10

10 <t<20

20 <t< 40

40 <t < 80 4

The mean time was calculated to be 27,5 minutes.

Calculate the
(a) value of f, [3]
(b) _ median time taken by the group on intemet and comment on

your answer, [3]
(c) standard deviation. [3]

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6 17 The data below are the times in seconds that fifteen students took to run an

800m race.

139 148 151 140 162
182 154 171 157 162
145 178 132 148 166

(a) @ Construct a stem and leaf diagram of the data.
G@) _ State any one advantage of a stem and leaf diagram.
b) @ Draw a box and whisker plot of the data.

(ii) _ State any one disadvantaged of the box and whisker
plot.

18 A continuous random variable X has the probability density function
given by

= O<x<1

f@= fret, 1sx<3

0, otherwise
where k is a constant.
(a) Find the value of k.
(b) Calculate the value of E(X)
() Find @ P(O8<xX<2)

Gi) PX>E(X))

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