Mathematics 9709 · AS & A Level · The normal distribution
The normal distribution — practice question
Pia jogs 2 km each day, and her recorded times, in minutes, are normally distributed with mean $10.1$ and standard deviation $1.3$.
(a)[3]
Determine the probability that, on a randomly selected day, Pia needs more than $11.3$ minutes to complete $2\text{ km}$.
(b)[3]
Pia takes longer than $t$ minutes to run $2\text{ km}$ on $75\%$ of days. Find $t$.
(c)[3]
How many days in a $90$-day period would you expect Pia to need between $8.9$ and $11.3$ minutes to run $2\text{ km}$?
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Valid standardisation shown $P\!\left(Z>\frac{11.3-10.1}{1.3}\right)=P(Z>0.9231)$” …