Potato seeds are packed in packets of 200 seeds, with on average 2% of the seeds in a packet rotten. A packet is substandard if it contains 5 or more rotten seeds. Using a Poisson approximation with mean $\lambda=200\times0.02=4$ , what is the probability that a packet is substandard, correct to 3 decimal places?

Model answer

0.371

Also accepted: 0.3711, 0.372

Explanation: With lambda = np = 4, P(X>=5) = 1 - P(X<=4) = 1 - e^(-4)(1+4+8+64/6+256/24) = 1 - 0.6288 = 0.3711.

Derived from ZIMSEC Statistics Paper 1, November 2018, Q6

Get the full paper, not just one question

Danho has every sitting for this paper, with your progress tracked question by question, offline.