Mathematics 9709 · AS & A Level · The normal distribution
The normal distribution — practice question
Obi’s times for walking to work each morning are modelled by a normal distribution with mean 14.8 minutes and standard deviation 1.5 minutes. He does this journey 5 days a week for 45 weeks in a year.
(a)[3]
State the probability that, on a randomly selected day, Obi spends more than 15.6 minutes walking to work.
(b)[3]
Find the value of $t$ if Obi spends more than $t$ minutes walking to work on 90% of days.
(c)[4]
How many days in a year would you expect Obi to spend within one minute of the mean walking time to work?
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$P(X>15.6)=P\left(Z>\frac{15.6-14.8}{1.5}\right)$” …