Mathematics 9709 · AS & A Level · The normal distribution

The normal distribution — practice question

The 13 00 service from Jahor to Keman operates every day. The chance that it reaches Keman late is $0.35$.
(a)[3]

From a random selection of 7 days, determine the probability that the train is late on fewer than 3 days.

(b)[5]

A random sample of 142 days is selected. Use an approximation to calculate the probability that the train is late on more than 40 days.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Binomial probabilities for $X=0,1,2$: $0.65^7+{}^7C_1(0.65^6)(0.35)+{}^7C_2(0.65^5)(0.35^2)$” …

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