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Cambridge International AS & A Level

CANDIDATE
NAME

CENTRE CANDIDATE
NUMBER NUMBER
*5715777126*

MATHEMATICS 9709/51
Paper 5 Probability & Statistics 1 October/November 2022

1 hour 15 minutes

You must answer on the question paper.

You will need: List of formulae (MF19)

INSTRUCTIONS
³ Answer all questions.
³ Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
³ Write your name, centre number and candidate number in the boxes at the top of the page.
³ Write your answer to each question in the space provided.
³ Do not use an erasable pen or correction fluid.
³ Do not write on any bar codes.
³ If additional space is needed, you should use the lined page at the end of this booklet; the question
number or numbers must be clearly shown.
³ You should use a calculator where appropriate.
³ You must show all necessary working clearly; no marks will be given for unsupported answers from a
calculator.
³ Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.

INFORMATION
³ The total mark for this paper is 50.
³ The number of marks for each question or part question is shown in brackets [ ].

This document has 12 pages. Any blank pages are indicated.

JC22 11_9709_51/RP
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1 The probability distribution table for a random variable X is shown below.

x −2 −1 0.5 1 2
P X = x
0.12 p q 0.16 0.3

Given that E X
= 0.28, find the value of p and the value of q. [4]

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2 The residents of Persham were surveyed about the reliability of their internet service. 12% rated the
service as ‘poor’, 36% rated it as ‘satisfactory’ and 52% rated it as ‘good’.

A random sample of 8 residents of Persham is chosen.

(a) Find the probability that more than 2 and fewer than 8 of them rate their internet service as poor
or satisfactory. [3]

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A random sample of 125 residents of Persham is now chosen.

(b) Use an approximation to find the probability that more than 72 of these residents rate their internet
service as good. [5]

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3 The Lions and the Tigers are two basketball clubs. The heights, in cm, of the 11 players in each of
their first team squads are given in the table.

Lions 178 186 181 187 179 190 189 190 180 169 196
Tigers 194 179 187 190 183 201 184 180 195 191 197

(a) Draw a back-to-back stem-and-leaf diagram to represent this information, with the Lions on the
left. [4]

(b) Find the median and the interquartile range of the heights of the Lions first team squad. [3]

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It is given that for the Tigers, the lower quartile is 183 cm, the median is 190 cm and the upper quartile
is 195 cm.

(c) Make two comparisons between the heights of the players in the Lions first team squad and the
heights of the players in the Tigers first team squad. [2]

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4 In a large population, the systolic blood pressure (SBP) of adults is normally distributed with
mean 125.4 and standard deviation 18.6.

(a) Find the probability that the SBP of a randomly chosen adult is less than 132. [2]

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The SBP of 12-year-old children in the same population is normally distributed with mean 117. Of
these children 88% have SBP more than 108.

(b) Find the standard deviation of this distribution. [3]

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Three adults are chosen at random from this population.

(c) Find the probability that each of these three adults has SBP within 1.5 standard deviations of the
mean. [4]

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5 A game is played with an ordinary fair 6-sided die. A player throws the die once. If the result is
2, 3, 4 or 5, that result is the player’s score and the player does not throw the die again. If the result
is 1 or 6, the player throws the die a second time and the player’s score is the sum of the two numbers
from the two throws.

(a) Draw a fully labelled tree diagram to represent this information. [2]

Events A and B are defined as follows.

A: the player’s score is 5, 6, 7, 8 or 9
B: the player has two throws

(b) Show that P A
= 13 . [3]

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(c) Determine whether or not events A and B are independent. [2]

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(d) Find P B | A′
. [3]

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6 A Social Club has 15 members, of whom 8 are men and 7 are women. The committee of the club
consists of 5 of its members.

(a) Find the number of different ways in which the committee can be formed from the 15 members
if it must include more men than women. [4]

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The 15 members are having their photograph taken. They stand in three rows, with 3 people in the
front row, 5 people in the middle row and 7 people in the back row.

(b) In how many different ways can the 15 members of the club be divided into a group of 3, a group
of 5 and a group of 7? [3]

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In one photograph Abel, Betty, Cally, Doug, Eve, Freya and Gino are the 7 members in the back row.

(c) In how many different ways can these 7 members be arranged so that Abel and Betty are next to
each other and Freya and Gino are not next to each other? [3]

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Additional Page

If you use the following lined page to complete the answer(s) to any question(s), the question number(s)
must be clearly shown.

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Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.

To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.

Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge
Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.

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