Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
The amount of time Rafa does homework each day during term-time is normally distributed with mean $1.9$ hours and standard deviation $\sigma$ hours. On $80\%$ of these days, he works on his homework for more than $1.35$ hours.
(i)[3]
Find $\sigma$.
(ii)[2]
Find the probability that Rafa spends under $2$ hours on his homework on a randomly chosen term-time day.
(iii)[6]
A random sample of $200$ days in term-time is taken. Use an approximation to find the probability that the number of days on which Rafa spends more than $1.35$ hours on his homework is between $163$ and $173$ inclusive.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate standard score $z=-0.842$ (rounded value allowed)” …