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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 Total
Marks 8 6 7 21
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 3 questions Question 1 Code: 9709/61/M/J/18/4, Topic: The normal distribution$\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.$[5]\text{(b)}$The random variable$X$has the distribution$\mathrm{N}\left(\mu, \sigma^{2}\right)$, where$3 \sigma=4 \mu$and$\mu \neq 0$. Find$\mathrm{P}(X<3 \mu)$.$[3]$Question 2 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.$[3]\text{(ii)}$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.$[3]$Question 3 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.$[3]\text{(ii)}$Find the probability that the group of 7 includes at least 2 girls.$[4]\$

Worked solutions: P1, P3 & P6 (S1)

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