Answer
It would be unusual to observe 20 patients who experience insomnia as a side effect. This is because 20 is more than 2 standard deviations away from the mean.
Work Step by Step
If the observation is at least 2 standard deviations away from the mean (less than μ−2σ or greater than μ+2σ) then it is considered unusual.
i) First, find the standard deviation
$\sqrt {np(1-p)}$
= $\sqrt {240 \times 0.05 \times (1-0.05)}$
= 3.376388603
$\approx$ 3.376
ii) Find μ−2σ and μ+2σ
μ−2σ = 12 - 2(3.376) = 5.248
μ+2σ = 12 + 2(3.376) = 18.752
Since 20 does not fall between 5.248 and 18.752, it is an unusual value.
