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Unit 14: Poisson Probability Distribution

14.5 Review Questions Notes

1. What is a ‘Poisson Process’? Obtain probability mass function of Poisson variate as a
limiting form of the probability mass function of binomial variate.

2. Obtain mean and standard deviation of a Poisson random variate. Discuss some business
and economic situations where Poisson probability model is appropriate.
3. How will you use Poisson distribution as an approximation to binomial? Explain with the
help of an example.
4. State clearly the assumptions under which a binomial distribution tends to Poisson
distribution.
5. A manufacturer, who produces medicine bottles, finds that 0.1% of the bottles are defective.
The bottles are packed in boxes containing 500 bottles. A drug manufacturer buys 100
boxes from the producer of the bottles. Use Poisson distribution to find the number of
boxes containing (i) no defective bottles (ii) at least two defective bottles.
6. A factory turning out lenses, supplies them in packets of 1,000. The packet is considered by
the purchaser to be unacceptable if it contains 50 or more defective lenses. If a purchaser
selects 30 lenses at random from a packet and adopts the criterion of rejecting the packet if
it contains 3 or more defectives, what is the probability that the packet (i) will be accepted,
(ii) will not be accepted?

7. 800 employees of a company are covered under the medical group insurance scheme.
Under the terms of coverage, 40 employees are identified as belonging to ‘High Risk’
category. If 50 employees are selected at random, what is the probability that (i) none of
them is in the high risk category, (ii) at the most two are in the high risk category? (You
may use Poisson approximation to Binomial).
8. The following table gives the number of days in 50 day-period during which automobile
accidents occurred in a certain part of the city. Fit a Poisson distribution to the data.

No. of accidents : 0 1 2 3 4
No. of days : 19 18 8 4 1
9. Comment on the following statements:

(a) The mean of a Poisson variate is 4 and standard deviation is 3 .
(b) The second raw moment of a Poisson distribution is 2. The probability P(X = 0)
-1
= e .
(c) If for a Poisson variate X, P(X = 1) = P(X = 2), then E(X) = 2.
-1
(d) If for a Poisson variate X, P(X = 0) = P(X = 1), then P(X > 0) = e .
10. A firm buys springs in very large quantities and from past records it is known that 0.2%
are defective. The inspection department sample the springs in batches of 500. It is required
to set a standard for the inspectors so that if more than the standard number of defectives
is found in a batch the consignment can be rejected with at least 90% confidence that the
supply is truly defective.

How many defectives per batch should be set as the standard?

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