Mathematics 9709 · AS & A Level · The normal distribution

The normal distribution — practice question

Davin’s daily time spent on his games machine is normally distributed, with mean $3.5$ and standard deviation $0.9$.
(a)[3]

Determine the probability that, on a randomly selected day, Davin spends more than $4.2$ hours on his games machine.

(b)[3]

On $90\%$ of days Davin spends more than $t$ hours on his games machine. Find the value of $t$.

(c)[3]

Estimate the number of days in a $365$-day year on which Davin spends between $2.8$ and $4.2$ hours on his games machine.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Apply standardisation $z=\\frac{4.2-3.5}{0.9}$

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