Mathematics 9709 · AS & A Level · The normal distribution
The normal distribution — practice question
In Molimba, adult males' heights, in cm, are normally distributed with mean $176\text{ cm}$ and standard deviation $4.8\text{ cm}$.
(a)[3]
Determine the probability that a randomly selected adult male in Molimba has a height above $170\text{ cm}$.
(b)[4]
$60\%$ of adult males in Molimba have a height between $170\text{ cm}$ and $k\text{ cm}$, where $k$ is greater than $170$. Determine the value of $k$, and give your answer correct to $1$ decimal place.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Converts $P(X>170)$ into standard form using $Z=\frac{170-176}{4.8}$” …