Mathematics 9709 · AS & A Level · The normal distribution

The normal distribution — practice question

For a particular region of the Arctic, the chance of snow on any one day is $0.7$, and this does not depend on any other day.
(a)[3]

Determine the probability that, over a week of 7 days, snow falls on at least five of them.

(b)[2]

A week that has snow on at least five of the seven days is described as a ‘white’ week. Determine the probability that, among three weeks selected at random, at least one is a white week.

(c)[5]

In another Arctic region, the probability that a week is white is $0.8$. Use a suitable approximation to determine the probability that, in 60 randomly selected weeks, fewer than 47 are white weeks.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Appropriate binomial model for $P(X=5,6,7)$ using $n=7$ and $p=0.7$.

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