Question

13. The table below shows the marks scored by some candidates in an examination. (a) Construct a cumulative frequency table for the distribution and draw a cumulative frequency curve. (b) Use the curve to estimate, correct to one decimal place: (i) the lowest mark for distinction if 5% of the candidates passed with distinction; (ii) the probability of selecting a candidate who scored at most 45%.

Accepted Answer

(a) Using the class boundaries and cumulative frequencies from the given mark distribution, an ogive (cumulative frequency curve) is plotted with marks on the x-axis and cumulative frequency on the y-axis.
(b)(i) With 200 candidates total, 5% pass with distinction means 95% (190 candidates) did not. Reading from the cumulative frequency curve at 190, the corresponding mark (lowest mark for distinction) is approximately 87.5%.
(ii) Reading the cumulative frequency at 45% from the curve gives approximately 70 candidates. Probability = 70/200 = 0.35 (1 d.p.).

WAEC Mathematics 2015 Theory — Question 22

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