Mathematics 9709 · AS & A Level · The normal distribution
The normal distribution — practice question
Raj wants to get fitter, so he runs each day. His run times, measured in minutes, are normally distributed with mean $41.2$ and standard deviation $3.6$.
(a)[3]
Find the probability that, on a randomly selected day, Raj runs for more than $43.2$ minutes.
(b)[2]
Find an estimate for how many days in a $365$-day year Raj runs for less than $43.2$ minutes.
(c)[3]
On $95\%$ of days, Raj runs for more than $t$ minutes. Find the value of $t$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “A correct standardisation is, for example, $P(X>43.2)=P\!\left(Z>\frac{43.2-41.2}{3.6}\right)=P(Z>0.5556)$.” …