The heights of boys at a particular school follow a normal distribution with a standard deviation of

Question

The heights of boys at a particular school follow a normal distribution with a standard deviation of 5 cm. The probability of a boy being shorter than 153 cm is 0.705.

Calculate the mean height of the boys.
Find the probability of a boy being taller than 156 cm.

[6]

Accepted Answer

$P(X>156)=P\!\left(Z>\frac{156-150.3}{5}\right)\approx0.127$.

Determine a normal mean from a percentile and calculate another tail probability.

Determine a normal mean from a percentile and calculate another tail probability.

Solution:

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