WAEC 2014 · Paper 2 · Q11

(a)
The probabilities that Manful, John and Ernest will pass an examination are $\frac23$ , $\frac58$ and $\frac34$ respectively. Find the probability that all three will pass the examination.
(b)
The scores of students in a test were recorded as follows:

4 2 1 6 5 3 5 6 1 2 1 5 5 6 3 4 3 5 1 5

(i) Construct a frequency distribution table. (ii) Represent the information in a bar chart. (iii) Calculate the interquartile range.

Worked solution (try it first)

(a)

The three results are independent, so multiply: $\frac23 \times \frac58 \times \frac34 = \frac{30}{96}$
$= \frac{5}{16}$ .

(b)(i)

Tally each score:
Score 1 2 3 4 5 6

Frequency 4 2 3 2 6 3
The frequencies add up to 20, the number of scores.

(ii)

The scores are separate whole numbers, so draw a bar chart: one bar for each score, all the same width, with gaps between them, and heights 4, 2, 3, 2, 6, 3.
Label the axes "Score" and "Frequency".

(iii)

In order, the 20 scores are $1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6$ .
$Q_1$ is at position $\frac{20}{4} = 5$ : the 5th score is 2.
$Q_3$ is at position $\frac{3 \times 20}{4} = 15$ : the 15th score is 5.
Interquartile range $= Q_3 - Q_1 = 5 - 2 = 3$ .

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