2018_stats_nov_paper1

Extracted Content: 2018_stats_nov_paper1

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"For Performance Measuremant

ZIMBABWE SCHOOL EXAMINATIONS COUNCIL

General Certificate of Education Advanced Level

STATISTICS .. 6046/1
PAPER 1

NOVEMBER 2018 SESSION 3 hours

Additional materials:
Answer paper
Graph paper
List of Formula

Scientific calculator

Ne eit
TIME 3 hours

a

INSTRUCTIONS TO CANDIDATES

Write your name, centre number ani candidate number in the spaces provided on the answer
paper/answer booklet.

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Answer all questions.

If a 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 correct to the nearest degree, and in
other cases it should be given correct to 2 significant figures.

ae a pee ee nn EE A NLT LCC RS CRAY tt tn on

| tNFORMATION FOR CANDIDATES ~
‘The number of marks is given in brackets [ ] at the end of each question or part question.
The total mimber of marks for this paper is 120.

Questions are printed in the order of their mark allocations.

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

} ” “This question paper consists of § printed pages and 2 blank pages.

Copyright: Zimbabwe Schooi Examinations Council, N2018.

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' The nse of a scientific ca'culator is expected, where appropriate. : |
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SZIMSEC N2018 {Turn over |

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B

below shows the frequency

he table

A group of twenty people played a game. T
distribution of their scores.

score (X)

nuraber of people

The mean score is 5.

Find
[2]

(a) the value of x,

(b) __ the variance of the distribution.

The head of a school wishes to contact parents of learners. She could use
e-mail, letter or cellphone with probabilities 0.4, 0.1 and 0.5 respectively.
She uses only one of the methods. The probabilities of the parents receiving
the message if the head uses e-mail, letter or cellphone are 0,6; 0,8 and

Jil respectively.

(a) Find the probability that ‘the parents receive the message. [2]

(b) Given that the parents received the message, find the probability that
they received it via email.

Les)
Lot

[4]

(a) List the four components of time series.

(b) State the effect on the pattern of plot, of using a 4 point moving average

compared to a 3-point moving average.

[2]

f the novels in a collection of 20 novels. A learner

(a) Julius Caesar is one ©
0 take for the holiday.

is going to choose 5 of these novels t

Find the

@) number of ways the learner can choose the 5 books, (2]
(i) number of choices that will include Julius Caesar.

(b) Find the number of ways in which 3 boys and 4 girls can standin a lve if

1}

2)

a there are no restrictions,

Gi) the boys stand next to each ovher.

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3

shows the frequency

e. The table below

A group of twenty people played a gam
distribution of their scores.

score (X)

nuraber of people

The mean score is 5.

Find

(a) the value of x,

(b) __ the variance of the distribution.

The head of a school wishes to contact parents of learners. She could use
e-mail, letter or cellphone with probabilities 0.4, 0.1 and 0.5 respectively.

She uses only one of the methods. The probabilities of the parents receiving
the message if the head uses e-mail, letter or cellphone are 0,6; 0,8 and

Jil respectively.

(a) Find the probability that the parents receive the message. [2]

(b) Given that the parents received the message, find the probability that
they received it via email.

(a) List the four components of time series. [4]
(b) State the effect on the pattern of plot, of using a 4 point moving average

compared to a 3-point moving average. [2]
(ay Julius Caesar is one of the novels in a collection of 20 novels. A learner

is going to choose 5 of these novels to take for the holiday.

Find the

(i) number of ways the learner can choose the 5 books, [2]

[2]

(ii) number of choices that will include Julius Caesar.
(b) Find the number of ways in which 3 boys and 4 girls can standin a ae if

(0) there are no restrictions,

Gi) the boys stand next to each ¢

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3

The random vari
variable X has Probability density function given by

3
m4 x?),~2 Sx<2

0 otherwise

Find
nd (a) E(X), a)

(b) —-Var(x) ; (4)

6 (a) State the conditions under which the Poisson distribution can be
used to approximate the Binomial distribution, [2]

(b) Potato seeds are packed in packets each containing 200 seeds. On
average 2 % of the seeds in a aie rai A packet containing
5 or more rotten potato seeds is said é substandard.

(i) Calculate the probability that a packet of potato seeds is
substandard. [3]

(ii) A load consists of 20 randomly chosen packets of potato seeds.

Find the probability that the load will consist of exactly 2
packets which are substandard. (3]

7 (a) Given that E(X) = 1,2 and Var(X) = 0,6 and that the random variable Y
: is defined by Y = 10X+50,

Sees

find
(i) E(Y). [1]

(ii) Var(Y). [2}

(b) A random sample consists of 160 independent observations of Y,

Find the probability that the sample mean (Y) lies between 61
ard 62,5. (5]

8 In a normal distribution with mean y and standard deviation G,
P(X >5.4) = 0,5 and P(X > 48) = 0.6554.

(a) Calculate the value of y and the value of a. [4]

(b) Lf 4 observations of X are taken at random from this distribution, find
the probability that at least 2 observations are greater than 4,8. [4]

6046/1 N2018
' [Turn over

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yx = 79.53 ; pd = 100.4621

Test at the 5 % level of significance, the claim that the pockets contain less
than 1,10 kg of manure,

10 The heights (cm) of 15 children were measured and the results shown below

(a)
(b)

(¢)

ia (a)

113 120 158 132 125
104 "142 160 145 104
162 V7 107 124 134

Draw a stem-and-leaf diagram to represent the heights
Find the

(i) median,

(ii) quartiles of the heights.

() Using a scale of 2.cm to represent a height of 10 cm, draw
a box and whisker plot for the data.

(ii) Comment on the distribution of these heights.

Events A and B are such that P(A U B) = 0.9, P(An B) = 0.2 and
P(A/B) = 0.8.

Find

@ P(B)

(ii) P(A’) where A’ is the complement of A.

An unbiased die is thrown until a six appears. Find the expected
number of tosses.

Define the following terms
(i) population,

(i) sample,

Bi) census.

© any twe.methods of obtaining an unbiased sample.

ANAGL MA018

The mass, x kg, of each pocket in @ random sample of 80 pockets filled with
manure was measured and the results summarised by

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qc) The amount of p

ocket mo
8Y was noted.

ney ($X i
‘The tens ($X) received by 120 |

ts were summarised by

XX ™~ 50} — —221

earners on visiting

; » 2X-50)2= 4708
Find

(i) unbiased estima:

1as\ tes of the population mean and standard
deviation,

[3]

(ii) 495 % confidence interval for the population mean of the
amount of money given to learners, [4]

13 The number of calls per hour to a H

was recorded with the results below.

arts on

Test at the 10% level of significance the claim that the number of calls per
hour follow a uniform distribution. [12]

otline during 9 am to 4 pm on weekdays

12 am -1 pm | 1-2pm

129 | 117

period

11-12 am

2-3 pm

number
of calls

14 (a) _—_ Define, with the aid of diagrams, the term correlation. — ” [4]

(b) Sales representatives make calls to potential customers in order to boost
.sales, The table below shows the number of calls to potential customers
made by each of 6 sales representatives and the sales turnover.

Sales representative

re

| Number of calls

Sales turnover ($1000)
L Saul

Calculate the

) product moment correlation coefficient and comment on the
relationship between number of. calls and sales turn over. [4]

(ii) least squares regression equation of sales turnover on number
of calls made. [4]

6046/1 N2018
lYurs over

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(c) Use the equation to find where possible the turnover for a sales representative who made

(i) 4 calls [3]

(ii) 10 calls 1]

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