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This is the Statistics revision pack. It is a free revision pack for revision.
NOVEMBER 2018 PAPER 1
1. A group of twenty people played a game. The table below shows the frequency distribution of their scores.
Score $(X)$ | 1 | 2 | 4 | $X$
Number of people | 2 | 5 | 7 | 6
The score mean is 5 . Find
a) the value of $x$,
[2]
b) the variance of the distribution.
[2]
2. The head of a school wishes to contact parents of learners. She could use e-mail, letter or cell phone with probabilities $0.4,0.1$ and 0.5 respectively. She uses only one of the methods. The probabilities of parents receiving the messages if the head uses e-mail, letter or cell phone are 0.6 , 0.8 and 1 respectively.
a) Find the probability that the parents receive the message.
[2]
b) Given that the parents receives the message, find the probability that they received it via e-mail.
[3]
3. a) List the four components of time series.
[4]
b) State the effect on the pattern of plot, of using a 4 point moving average compared to a 3 point moving average.
[2]
4. a) Julias Caeser is one of the novels in a collection of 20 novels. A learner is going to choose 5 of these novels to take for the holiday. Find the
i) number of ways the learner can choose the 5 books,
[2]
ii) number of choices that will include Julias Caeser.
[2]
b) Find the number of ways in which 3 boys and 4 girls can stand in a line if
i) three are no restrictions.
[1]
ii) the boys stand next to each other.
[2]
5. The random variable X has probability density function given by $f(x)=\left\{\begin{array}{cc}\frac{3}{32}\left(4-x^{2}\right), | -2 \leq x \leq 2 0, | \text { otherwise }\end{array}\right.$
Find
a) $E(X)$,
[3]
b) $\operatorname{Var}(\mathrm{X})$
[4]
6. a) State the condition under which the Poisson distribution can be used to approximate the Binomial distribution.
[2]
b) Potato seeds are packed in packets each containing 200 seeds. On average $2 \%$ of the seeds in a packet are rotten. A packet containing 5 or more rotten potatoes is said to be substandard.
i) Calculate the probability that a packet of potato seeds is substandard.
[3]
ii) A load consist of 20 randomly chosen packets of potato seeds. Find the probability that the load will consist of exactly 2 packets which are substandard.
[3]
7. a) Given that $E(X)=1,2$ and $\operatorname{Var}(X)=0,6$ and that the random variable $Y$ is defined by $Y=10 X+50$, find
i) $\mathrm{E}(\mathrm{Y})$,
[1]
ii) $\operatorname{Var}((\mathrm{X})$.
[2]
b) A random sample consist of 160 independent observations of Y. Find the …