Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

A survey carried out at one large college found that the fraction of students who own a car is $\frac{1}{4}$.
(i)[3]

Five students from the college are selected at random. Find the probability that at least four of them own a car.

(ii)[3]

For a random sample of $n$ students at the college, the chance that at least one student owns a car is greater than 0.995. Find the least possible value of $n$.

(iii)[4]

For a random sample of $160$ students at the college, use a suitable approximate distribution to find the probability that fewer than $50$ of them own a car.

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