Discussion
The height of adult men in a population follows normal distribution with mean 1.65 meters and standard deviation \(\sigma\). If 40% of the men are shorter than 1.5 meters, the percentage of population which is taller than 1.80 meters is :
Answer: C
The percentage taller than 1.80 m is 40%.
The normal distribution is symmetric about its mean 1.65. The heights 1.50 and 1.80 are equally far from the mean, 0.15 m below and above. So
\[ P(X \gt 1.80) = P(X \lt 1.50) = 0.40 \]
The value of \(\sigma\) is not needed. 60% is the proportion shorter than 1.80 m, and 80% doubles the wrong tail.
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