Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
For people living in one town, the time needed to cook an egg follows a normal distribution with mean $4.2$ minutes and standard deviation $0.6$ minutes.
(i)[3]
Find the probability that a randomly selected person needs between $3.5$ and $4.5$ minutes to cook an egg.
(ii)[3]
$12\%$ of people need longer than $t$ minutes to cook an egg. Find the value of $t$.
(iii)[3]
A random sample of $n$ people is taken. Find the smallest possible value of $n$ if the probability that none of these people takes more than $t$ minutes to cook an egg is below $0.003$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use standardisation to write $P(X<4.5)=P\left(Z<\dfrac{4.5-4.2}{0.6}\right)$” …