(a)[3]
Find the probability that a member selected at random from the club takes between $56$ and $66$ seconds to swim $100$ metres.
(b)[3]
$13\%$ of the members of the club take more than $t$ minutes to swim $100$ metres. Determine $t$.
Mathematics 9709 · AS & A Level · The normal distribution
The normal distribution — practice question
The times that members of a large swimming club need to swim 100 metres are normally distributed, with mean $62$ seconds and standard deviation $5$ seconds.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Standardise to obtain $P(56<X<66)=P\left(\frac{56-62}{5}<Z<\frac{66-62}{5}\right)=P(-1.2<Z<0.8)$” …
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