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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 |
Question 1 Code: 9709/72/O/N/13/1, Topic: -
71Question 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: -
71Question 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: -