Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
Fiona uses her calculator to generate $12$ random integers from $7$ to $21$, inclusive. The random variable $X$ counts how many of the $12$ integers are multiples of $5$.
(i)[3]
State the distribution of $X$ and specify its parameters.
(ii)[3]
Calculate the probability that $X$ lies between $3$ and $5$, inclusive.
(iii)[3]
Fiona now generates $n$ random integers between $7$ and $21$ inclusive. Find the least possible value of $n$ if the probability that none of these integers is a multiple of $5$ is less than $0.01$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State that $X \sim \text{Bin}(12, 0.2)$” …