Financial Risk Manager Part 1
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The mean height of female FRM exam candidates over the years is 1.671m while that of male candidates is 1.757. Given that the mean height of ALL of the exam candidates is 1.712m, calculate the percentage of the candidates who are female:
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Explanation:
Let F be the proportion of females.
Applying the idea of a weighted mean,
1.671F + 1.757(1-F) = 1.712
⇒ 1.671F + 1.757 - 1.757F = 1.712
⇒ 1.757 - 1.712 = 1.757F - 1.671F
⇒ 0.045 = 0.086F
⇒ F = 0.523 or 52.3%
1.671F + 1.757(1-F) = 1.712
⇒ 1.671F + 1.757 - 1.757F = 1.712
⇒ 1.757 - 1.712 = 1.757F - 1.671F
⇒ 0.045 = 0.086F
⇒ F = 0.523 or 52.3%
This is a weighted average problem where we need to find the proportion of female candidates (F) such that the weighted average of female and male heights equals the overall mean height. The solution shows that 52.3% of the candidates are female.
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