Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
Wendy’s commute to work has three stages: she walks to the train station, travels by train, and then walks to the office. The times, measured in minutes, for those three stages are independent and follow the distributions $N(15.0, 1.1^2)$, $N(32.0, 3.5^2)$ and $N(8.6, 1.2^2)$ respectively.
(a)[2]
Calculate the mean and variance for the total time Wendy’s journey takes.
(b)[3]
If Wendy’s journey lasts more than $60$ minutes, she is late for work. Find the probability that, on a randomly selected day, Wendy will be late for work.
(c)[3]
Find the probability that the mean of Wendy’s journey times over $15$ randomly chosen days will be less than $54.5$ minutes.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Mean is $15.0+32.0+8.6=55.6$” …