Mathematics 9709 · AS & A Level · Discrete random variables

Discrete random variables — practice question

Residents of Mahjing were surveyed and asked to sort their local bus service: 25% of residents described the service as good. 60% of residents described the service as satisfactory. 15% of residents described the service as poor.
(a)[5]

A random sample of $110$ residents of Mahjing is selected. Find the probability, using a suitable approximation, that fewer than $22$ residents said their bus service was good.

(b)[3]

For a random sample of $10$ residents of Mahjing, find the probability that fewer than $8$ rated their bus service as good or satisfactory.

(c)[2]

Three residents of Mahjing are chosen at random. Find the probability that one resident classified the bus service as good, one as satisfactory, and one as poor.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Mean correctly found as $110\times0.25=27.5$ and variance correctly found as $110\times0.25\times0.75=20.625$

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