Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
The random variable $X$ has distribution $X \sim N(82, 126)$.
(i)[3]
A value of $X$ is selected at random and then rounded to the nearest whole number. Find the probability that this whole number is $84$.
(ii)[4]
Five independent observations of $X$ are taken. Find the probability that no more than one of them is greater than $87$.
(iii)[5]
Determine the value of $k$ such that $P(87 < X < k) = 0.3$.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate standardisation with $\sqrt{126}$ at $83.5$ or $84.5$” …