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### HENRYTAIGO

#### Cambridge International AS and A Level

 Name of student HENRYTAIGO Date Adm. number Year/grade HenryTaigo Stream HenryTaigo 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 10 9 11 9 9 9 57
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 6 questions Question 1 Code: 9709/61/M/J/15/6, Topic: The normal distribution$\text{(i)}$In a certain country,$68 \%$of households have a printer. Find the probability that, in a random sample of 8 households, 5,6 or 7 households have a printer.$[4]\text{(ii)}$Use an approximation to find the probability that, in a random sample of 500 households, more than 337 households have a printer.$[5]\text{(iii)}$Justify your use of the approximation in part$\text{(ii)}$.$[1]$Question 2 Code: 9709/62/M/J/15/6, Topic: Permutations and combinations$\text{(a)}$Find the number of different ways the 7 letters of the word BANANAS can be arranged$\text{(i)}$if the first letter is$\mathrm{N}$and the last letter is$\mathrm{B}$,$[3]\text{(ii)}$if all the letters$\mathrm{A}$are next to each other.$[3]\text{(b)}$Find the number of ways of selecting a group of 9 people from 14 if two particular people cannot both be in the group together.$[3]$Question 3 Code: 9709/63/M/J/15/6, Topic: Representation of data Seventy samples of fertiliser were collected and the nitrogen content was measured for each sample. The cumulative frequency distribution is shown in the table below. $$\begin{array}{|l|c|c|c|c|c|c|} \hline \text{Nitrogen content} & \leqslant 3.5 & \leqslant 3.8 & \leqslant 4.0 & \leqslant 4.2 & \leqslant 4.5 & \leqslant 4.8 \\ \hline \text{Cumulative frequency} & 0 & 6 & 18 & 41 & 62 & 70 \\ \hline \end{array}$$$\text{(i)}$On graph paper draw a cumulative frequency graph to represent the data.$[3]\text{(ii)}$Estimate the percentage of samples with a nitrogen content greater than$4.4.[2]\text{(iii)}$Estimate the median.$[1]\text{(iv)}$Construct the frequency table for these results and draw a histogram on graph paper.$[5]$Question 4 Code: 9709/61/O/N/15/6, Topic: Probability Nadia is very forgetful. Every time she logs in to her online bank she only has a$40 \%$chance of remembering her password correctly. She is allowed 3 unsuccessful attempts on any one day and then the bank will not let her try again until the next day.$\text{(i)}$Draw a fully labelled tree diagram to illustrate this situation.$[2]\text{(ii)}$Let$X$be the number of unsuccessful attempts Nadia makes on any day that she tries to$\log$in to her bank. Copy and complete the following table to show the probability distribution of$X$.$[4]$$$\begin{array}{|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 \\ \hline \mathrm{P}(X=x) & & 0.24 & & \\ \hline \end{array}$$$\text{(iii)}$Calculate the expected number of unsuccessful attempts made by Nadia on any day that she tries to$\log$in.$[3]$Question 5 Code: 9709/62/O/N/15/6, Topic: Discrete random variables A fair spinner$A$has edges numbered$1,2,3,3$. A fair spinner$B$has edges numbered$-3,-2,-1,1$. Each spinner is spun. The number on the edge that the spinner comes to rest on is noted. Let$X$be the sum of the numbers for the two spinners.$\text{(i)}$Copy and complete the table showing the possible values of$X$.$[1]\text{(ii)}$Draw up a table showing the probability distribution of$X$.$[3]\text{(iii)}$Find$\operatorname{Var}(X)$.$[3]\text{(iv)}$Find the probability that$X$is even, given that$X$is positive.$[2]$Question 6 Code: 9709/63/O/N/15/6, Topic: Representation of data The heights to the nearest metre of 134 office buildings in a certain city are summarised in the table below. $$\begin{array}{|l|c|c|c|c|c|} \hline \text{Height (m)} & 21-40 & 41-45 & 46-50 & 51-60 & 61-80 \\ \hline \text{Frequency} & 18 & 15 & 21 & 52 & 28 \\ \hline \end{array}$$$\text{(i)}$Draw a histogram on graph paper to illustrate the data.$[4]\text{(ii)}$Calculate estimates of the mean and standard deviation of these heights.$[5]\$

Worked solutions: P1, P3 & P6 (S1)

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