Mathematics 9709 · AS & A Level · The normal distribution
The normal distribution — practice question
Many runners entered two charity runs to collect money for a new community centre. In the first run, the finishing times were normally distributed with mean 46.3 seconds and standard deviation 6.4 seconds. In the second run, the finishing times were normally distributed with mean 39.8 seconds and standard deviation of $\sigma$ seconds. 10% of the runners took more than 48.6 seconds.
(a)[3]
Find the chance that a runner selected at random needed more than 55.1 seconds to complete the run.
(b)[3]
Determine the value of $\sigma$.
(c)[5]
From the second run, 150 runners are selected at random. Use an approximation to find the probability that fewer than 20 of these 150 runners took more than 48.6 seconds to finish the run.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$P(X>55.1)=P\!\left(Z>\frac{55.1-46.3}{6.4}\right)=P(Z>1.375)$” …