WAEC 2017 · Paper 2 · Q12

Marks	0–2	3–5	6–8	9–11	12–14	15–17
Number of students	5	6	$\frac p3 + 5$	8	$\frac23p + 2$	1

The table shows the marks scored by 30 students in a class test. Find:

(a)
the value of $p$ ;
(b)
correct to two decimal places, the variance of the distribution, using an assumed mean of 7;
(c)
the probability of obtaining at most 11 in the class test.

Worked solution (try it first)

(a)

The frequencies add to 30: $5 + 6 + \frac p3 + 5 + 8 + \frac23p + 2 + 1 = 30$ , so $27 + p = 30$ and $p = 3$ .

(b)

The frequencies are $5, 6, 6, 8, 4, 1$ and the class marks $1, 4, 7, 10, 13, 16$ .
With $d = x - 7$ : $\sum fd = 9$ and $\sum fd^2 = 531$ .
Variance $= \dfrac{531}{30} - \left(\dfrac{9}{30}\right)^2$
$= 17.7 - 0.09$
$= 17.61$ .

(c)

At most 11 covers the first four classes: $\dfrac{5 + 6 + 6 + 8}{30} = \dfrac{25}{30}$
$= \dfrac56$ .

Report a problem with this question