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JANNA CREAMER

Cambridge International AS and A Level

Name of student JANNA CREAMER Date
Adm. number 0 Year/grade Stream
Subject Probability & Statistics 1 (S1) Variant(s) P61, P62, P63
Start time Duration Stop time

Qtn No. 1 2 3 4 5 6 Total
Marks 7 8 9 9 9 8 50
Score

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Question 1 Code: 9709/61/M/J/15/5, Topic: Representation of data

The table shows the mean and standard deviation of the weights of some turkeys and geese.

$$ \begin{array}{|l|c|c|c|} \hline & \text{Number of birds} & \text{Mean (kg)} & \text{Standard deviation (kg)} \\ \hline \text{Turkeys} & 9 & 7.1 & 1.45 \\ \hline \text{Geese} & 18 & 5.2 & 0.96 \\ \hline \end{array} $$

$\text{(i)}$ Find the mean weight of the 27 birds. $[2]$

$\text{(ii)}$ The weights of individual turkeys are denoted by $x_{t}$ kg and the weights of individual geese by $x_{g}$ kg. By first finding $\Sigma x_{t}^{2}$ and $\Sigma x_{g}^{2}$, find the standard deviation of the weights of all 27 birds. $[5]$

Question 2 Code: 9709/62/M/J/15/5, Topic: Probability

A box contains 5 discs, numbered $1,2,4,6,7$. William takes 3 discs at random, without replacement, and notes the numbers on the discs.

$\text{(i)}$ Find the probability that the numbers on the 3 discs are two even numbers and one odd number. $[3]$

The smallest of the numbers on the 3 discs taken is denoted by the random variable $S$.

$\text{(ii)}$ By listing all possible selections ( 126,246 and so on) draw up the probability distribution table for $S$. $[5]$

Question 3 Code: 9709/63/M/J/15/5, Topic: The normal distribution

The heights of books in a library, in $\mathrm{cm}$, have a normal distribution with mean $21.7$ and standard deviation 6.5. A book with a height of more than $29 \mathrm{~cm}$ is classified as 'large'.

$\text{(i)}$ Find the probability that, of 8 books chosen at random, fewer than 2 books are classified as large. $[6]$

$\text{(ii)}$ $n$ books are chosen at random. The probability of there being at least 1 large book is more than $0.98$. Find the least possible value of $n$. $[3]$

Question 4 Code: 9709/61/O/N/15/5, Topic: Permutations and combinations

$\text{(a)}$ Find the number of ways in which all nine letters of the word TENNESSEE can be arranged

$\text{(i)}$ if all the letters $\mathrm{E}$ are together, $[3]$

$\text{(ii)}$ if the $\mathrm{T}$ is at one end and there is an $\mathrm{S}$ at the other end. $[3]$

$\text{(b)}$ Four letters are selected from the nine letters of the word VENEZUELA. Find the number of possible selections which contain exactly one $\mathrm{E}$. $[3]$

Question 5 Code: 9709/62/O/N/15/5, Topic: Representation of data

The weights, in kilograms, of the 15 rugby players in each of two teams, $A$ and $B$, are shown below.

$$ \begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline \text{Team A} & 97 & 98 & 104 & 84 & 100 & 109 & 115 & 99 & 122 & 82 & 116 & 96 & 84 & 107 & 91 \\ \hline \text{Team B} & 75 & 79 & 94 & 101 & 96 & 77 & 111 & 108 & 83 & 84 & 86 & 115 & 82 & 113 & 95 \\ \hline \end{array} $$

$\text{(i)}$ Represent the data by drawing a back-to-back stem-and-leaf diagram with team $A$ on the lefthand side of the diagram and team $B$ on the right-hand side. $[4]$

$\text{(ii)}$ Find the interquartile range of the weights of the players in team $A$. $[2]$

$\text{(iii)}$ A new player joins team $B$ as a substitute. The mean weight of the 16 players in team $B$ is now $93.9 \mathrm{~kg}$. Find the weight of the new player. $[3]$

Question 6 Code: 9709/63/O/N/15/5, Topic: Permutations and combinations

$\text{(a)}$ Find the number of different ways that the 13 letters of the word ACCOMMODATION can be arranged in a line if all the vowels (A, I, O) are next to each other. $[3]$

$\text{(b)}$ There are 7 Chinese, 6 European and 4 American students at an international conference. Four of the students are to be chosen to take part in a television broadcast. Find the number of different ways the students can be chosen if at least one Chinese and at least one European student are included. $[5]$

Worked solutions: P1, P3 & P6 (S1)

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