Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

In one country, 60% of mobile phones sold come from Company A, 35% come from Company B, and the remaining 5% are produced by other firms.
(a(i))[3]

Determine the probability that, in a random group of 13 people who purchase a mobile phone, fewer than 11 pick a phone made by Company A.

(a(ii))[5]

Use a suitable approximation to work out the probability that, in a random sample of 130 people who buy a mobile phone, at least 50 choose a phone made by Company B.

(i)[3]

Determine the probability that, in a random group of $13$ people who purchase a mobile phone, fewer than $11$ pick a phone made by Company A.

(ii)[5]

Use a suitable approximation to work out the probability that, in a random sample of 130 people who buy a mobile phone, at least 50 choose a phone made by Company B.

(iii)[3]

A random sample of $n$ mobile phones sold is selected. The chance that at least one of these phones is made by Company B is greater than $0.98$. Determine the least possible value of $n$.

Worked solution & mark scheme

This 19-mark question has a full step-by-step worked solution and mark scheme. One marking point: A correct binomial setup for $P(X<11)$, or an equivalent form

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