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### THOMASCAUPE

#### Cambridge International AS and A Level

 Name of student THOMASCAUPE Date Adm. number Year/grade 1986 Stream ThomasCaupe 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 8 6 7 8 6 7 42
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 6 questions Question 1 Code: 9709/61/M/J/18/4, Topic: The normal distribution$\text{(a)}$The distance that car tyres of a certain make can travel before they need to be replaced has a normal distribution. A survey of a large number of these tyres found that the probability of this distance being more than$36800 \mathrm{~km}$is$0.0082$and the probability of this distance being more than$31000 \mathrm{~km}$is$0.6915.$Find the mean and standard deviation of the distribution.$\text{(b)}$The random variable$X$has the distribution$\mathrm{N}\left(\mu, \sigma^{2}\right)$, where$3 \sigma=4 \mu$and$\mu \neq 0$. Find$\mathrm{P}(X<3 \mu)$.$$Question 2 Code: 9709/62/M/J/18/4, Topic: Discrete random variables Mrs Rupal chooses 3 animals at random from 5 dogs and 2 cats. The random variable$X$is the number of cats chosen.$\text{(i)}$Draw up the probability distribution table for$X$.$\text{(ii)}$You are given that$\mathrm{E}(X)=\frac{6}{7}$. Find the value of$\operatorname{Var}(X)$.$$Question 3 Code: 9709/63/M/J/18/4, Topic: Representation of data Farfield Travel and Lacket Travel are two travel companies which arrange tours abroad. The numbers of holidays arranged in a certain week are recorded in the table below, together with the means and standard deviations of the prices. $$\begin{array}{|l|c|c|c|} \hline & \text{Number of holidays} & \text{Mean price (\)} & \text{Standard deviation (\)} \\ \hline \text{Farfield Travel} & 30 & 1500 & 230 \\ \hline \text{Lacket Travel} & 21 & 2400 & 160 \\ \hline \end{array}$$$\text{(i)}$Calculate the mean price of all 51 holidays.$\text{(ii)}$The prices of individual holidays with Farfield Travel are denoted by$\$x_{F}$ and the prices of individual holidays with Lacket Travel are denoted by $\$ x_{L}.$By first finding$\Sigma x_{F}^{2}$and$\Sigma x_{L}^{2}$, find the standard deviation of the prices of all 51 holidays.$$Question 4 Code: 9709/61/O/N/18/4, Topic: The normal distribution$\text{(a)}$It is given that$X \sim \mathrm{N}(31.4,3.6)$. Find the probability that a randomly chosen value of$X$is less than$29.4$.$\text{(b)}$The lengths of fish of a particular species are modelled by a normal distribution. A scientist measures the lengths of 400 randomly chosen fish of this species. He finds that 42 fish are less than$12 \mathrm{~cm}$long and 58 are more than$19 \mathrm{~cm}$long. Find estimates for the mean and standard deviation of the lengths of fish of this species.$$Question 5 Code: 9709/62/O/N/18/4, Topic: Permutations and combinations$\text{(i)}$Find the number of different ways that 5 boys and 6 girls can stand in a row if all the boys stand together and all the girls stand together.$\text{(ii)}$Find the number of different ways that 5 boys and 6 girls can stand in a row if no boy stands next to another boy.$$Question 6 Code: 9709/63/O/N/18/4, Topic: Permutations and combinations Out of a class of 8 boys and 4 girls, a group of 7 people is chosen at random.$\text{(i)}$Find the probability that the group of 7 includes one particular boy.$\text{(ii)}$Find the probability that the group of 7 includes at least 2 girls.$\$

Worked solutions: P1, P3 & P6 (S1)

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