Question 1

Paper 1, no calculatorHard6 marks

In a production run, the number of packets with faulty seals is modelled by X∼B(n,p)X\sim B(n,p) where nn and pp are unknown. The mean of XX is 33 and its variance is 2.12.1

(a)

Determine nn and pp

[4]
(b)

In a separate check, an inspector selects 10 packets without replacement from a lot of 20 packets, of which exactly 6 have faulty seals. A supervisor uses the values of nn and pp from part (a) to model the number of faulty packets in the check. Comment on whether this is appropriate.

[2]

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