WAEC 2016 · Paper 2 · Q13

(a)
Using an assumed mean of 40, find the standard deviation of the following set of numbers: 28, 31, 32, 37, 40, 42, 45, 46, 48 and 50.
(b)
A bag contains 50 identical balls, of which 15 are red and the rest green. Six balls are selected at random from the bag, one after the other, with replacement. Find, correct to two decimal places, the probability that: (i) exactly 4 red balls are selected; (ii) an equal number of red and green balls are selected; (iii) at least 2 green balls are selected.
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

Take $d = x - 40$ : the deviations add to $\sum d = -1$ and their squares to $\sum d^2 = 527$ .
$\sigma = \sqrt{\dfrac{\sum d^2}{n} - \left(\dfrac{\sum d}{n}\right)^2}$
$= \sqrt{52.7 - 0.01}$
$\approx 7.26$ .

With replacement, $p(\text{red}) = \frac{15}{50} = 0.3$ on every draw, with $n = 6$ .

At least 2 green means at most 4 red: $1 - [P(5 \text{ red}) + P(6 \text{ red})] = 1 - (0.0102 + 0.0007)$
$\approx 0.99$ .