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### MATHEMATICS 9709

#### Cambridge International AS and A Level

 Name of student Date Adm. number Year/grade Stream Subject Probability & Statistics 2 (S2) Variant(s) P72, P73 Start time Duration Stop time

Qtn No. 1 2 3 4 5 6 Total
Marks 4 5 3 5 9 8 34
Score

Get Mathematics 9709 Topical Questions (2010-2021) $14.5 per Subject. Attempt all the 6 questions Question 1 Code: 9709/72/O/N/13/1, Topic: - 71 Question 2 Code: 9709/73/O/N/15/1, Topic: - It is known that the number,$N$, of words contained in the leading article each day in a certain newspaper can be modelled by a normal distribution with mean 352 and variance 29. A researcher takes a random sample of 10 leading articles and finds the sample mean,$\bar{N}$, of$N$.$\text{(i)}$State the distribution of$\bar{N}$, giving the values of any parameters.$[2]\text{(ii)}$Find$\mathrm{P}(\bar{N}>354)$.$[3]$Question 3 Code: 9709/72/O/N/16/1, Topic: - 71 Question 4 Code: 9709/72/O/N/11/2, Topic: - Question 5 Code: 9709/73/O/N/12/6, Topic: - Darts are thrown at random at a circular board. The darts hit the board at distances$X$centimetres from the centre, where$X$is a random variable with probability density function given by $$\mathrm{f}(x)= \begin{cases}\dfrac{2}{a^{2}} x & 0 \leqslant x \leqslant a \\ 0 & \text { otherwise }\end{cases}$$ where$a$is a positive constant.$\text{(i)}$Verify that$\mathrm{f}$is a probability density function whatever the value of$a$.$[3]$It is now given that$\mathrm{E}(X)=8$.$\text{(ii)}$Find the value of$a$.$[3]\text{(iii)}$Find the probability that a dart lands more than$6 \mathrm{~cm}$from the centre of the board.$[3]\$

Question 6 Code: 9709/72/O/N/13/6, Topic: -

Worked solutions: P1, P3 & P6 (S1)

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