Mathematics 9709 · AS & A Level · Continuous random variables

Continuous random variables — practice question

The heights of books in a library, measured in cm, follow a normal distribution with mean $21.7$ and standard deviation $6.5$. Any book taller than $29$ cm is described as ‘large’.
(i)[6]

Find the probability that, from $8$ books selected at random, fewer than $2$ of them are classified as large.

(ii)[3]

With $n$ books chosen at random, the probability that there is at least $1$ large book exceeds $0.98$. Determine the smallest possible value of $n$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Standardising gives: $P(\text{large})=1-\Phi\left(\dfrac{29-21.7}{6.5}\right)$

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