Study Mathematics revision pack on Statistics for A-Level. Useful for revision, homework, and exam preparation in Zimbabwe.
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This is the ZIMSEC A-Level Mathematics revision pack for Paper 4. It is a free revision pack for revision.
2003 November paper 4
1. A Domestic workers Union claims that the average the average hourly rate paid to domestic workers is $$ 15,85$. The house-wife league in this country wishes to test this claim. They conducted a survey amongst a sample of 1225 domestic workers throughout the country. They found that sample mean hourly rate to be $$ 16,03$. Assume the population standard deviation of hourly rates paid to domestic workers is $$ 2,87$. Test the hypothesis at the $2 \%$ significance level that the average hourly rate paid to domestic workers in this country is more than $$ 15,85$.
[6]
2. Two players $A$ and $B$ take turns to toss a tetrahedral die until a 4 appear. A person who first throws a 4 wins the game. Assuming that $A$ throws first, Find
i) the average number of tosses required before a game is lost. [2]
ii) the probability that A wins the game. [5]
3. It is given that about $95 \%$ of values of a standard normal distribution lies between $a$ and $b$, where $\mathrm{a}<\mathrm{b}$ and $\mathrm{P}(\mathrm{a}<\mathrm{x}<\mathrm{b})=0,95$
i) Show that $b=\mu+1,96 \sigma$ and $a=\mu-1.96 \sigma$
[5]
ii) Hence show that $\mu=\frac{a+b}{2}$
[2]
4. A random sample of male and females indicated their views on a national dress as summarised below
| In favour | Opposed | Undecided | Total
Women | 118 | 62 | 25 | 205
Men | 84 | 78 | 37 | 199
Total | 202 | 140 | 62 | 404
At the $1 \%$ level of significance, test the hypothesis that there is no difference in opinion between men and women in as far as this survey is concerned.
[7]
5. On any day, the amount of time measured in hours, that a viler spends watching television is a continuous random variable T , with a cumulative distribution function given by
\[
F(t)=\left\{\begin{array}{l}
0
1-k(15-t)^{2}
1
\end{array}\right.
\]
$\mathrm{t} \leq 0$
$0 \leq t \leq 15$ where $k$ is a constant.
$\mathrm{t} \geq 15$
i) Show that $k=\frac{1}{225}$
[2]
ii) Show that for $0 \leq t \leq 15$, the probability density function of $T$ is given by $f(t)=\frac{2}{15}-\frac{2}{225} t[2]$
iii) Find the median $T$.
[3]
6. Twenty- three people in a random sample were asked to record the number of kilometres they travelled by bus in a given week. The distances to the nearest kilometre are shown below.
\[
6776854293489346526370724466877847665072825658
\]