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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

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 6 questions 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)}$Find the mean weight of the 27 birds.$\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.$$Question 2 Code: 9709/62/M/J/15/5, Topic: Probability A box contains 5 discs, numbered$1,2,4,6,7$. William takes 3 discs at random, without replacement, and notes the numbers on the discs.$\text{(i)}$Find the probability that the numbers on the 3 discs are two even numbers and one odd number.$$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$S$.$$Question 3 Code: 9709/63/M/J/15/5, Topic: The normal distribution The heights of books in a library, in$\mathrm{cm}$, have a normal distribution with mean$21.7$and standard deviation 6.5. A book with a height of more than$29 \mathrm{~cm}$is classified as 'large'.$\text{(i)}$Find the probability that, of 8 books chosen at random, fewer than 2 books are classified as large.$\text{(ii)}n$books are chosen at random. The probability of there being at least 1 large book is more than$0.98$. Find the least possible value of$n$.$$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,$\text{(ii)}$if the$\mathrm{T}$is at one end and there is an$\mathrm{S}$at the other end.$\text{(b)}$Four letters are selected from the nine letters of the word VENEZUELA. Find the number of possible selections which contain exactly one$\mathrm{E}$.$$Question 5 Code: 9709/62/O/N/15/5, Topic: Representation of data The weights, in kilograms, of the 15 rugby players in each of two teams,$A$and$B$, are shown below. $$\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}$$$\text{(i)}$Represent the data by drawing a back-to-back stem-and-leaf diagram with team$A$on the lefthand side of the diagram and team$B$on the right-hand side.$\text{(ii)}$Find the interquartile range of the weights of the players in team$A$.$\text{(iii)}$A new player joins team$B$as a substitute. The mean weight of the 16 players in team$B$is now$93.9 \mathrm{~kg}$. Find the weight of the new player.$$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.$\text{(b)}$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.$\$

Worked solutions: P1, P3 & P6 (S1)

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