Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

Robert’s calculator is used to produce 5 random integers from 1 to 9 inclusive.
(i)[3]

Find the probability that at least 2 of the 5 integers are less than or equal to $4$.

(ii)[4]

Robert now produces $n$ random integers from 1 to 9 inclusive. The random variable $X$ counts how many of these $n$ integers are less than or equal to an integer $k$ between $1$ and $9$ inclusive. It is given that the mean of $X$ is $96$ and the variance of $X$ is $32$. Determine the values of $n$ and $k$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Take $p=\frac{4}{9}$ or $\frac{5}{9}$

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