Poisson
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Preyosi DharProblems on Poisson Distribution
1. In a certain factory turning out razor blades there is a small chance 1/500 for any blade
to be defective. The blades are supplied in packets of 10. Calculate approximately the
number of packets containing at least two defective blades in a consignment of 10,000
packets.
2. Books from a certain publisher contain an average of 1 misprint per page. What is the
probability that on at least one page in a 300 page book from this publisher there will be
at least 5 misprints?
3. Suppose the rain falling at an average rate of 30 drops per square inch per minute. What
is the chance that a particular square inch is not hit by by any drops during a given 10
second period?
4. A car hire firm has two cars , which are hired out by the day. It has been that the number
of demands for cars of the firm on any day has a Poisson distribution with mean 1.5.
(a) Calculate the proportion of days on which neither car is used and the proportion of
days on which some demand is refused.
(b) If the two cars are used an equal number of times on the average, on what proportion
of days is a given one of the cars not in use ?
(c) How many cars should the firm have so as to meet all demands on approximately
98% of days ?
5. When the first proof of a book containing 250 pages was read, the following distribution
of misprints was obtained
Number of
misprints per page 0 1 2 3 4 5 ≥6
Frequency 139 76 28 4 2 1 0
Fit an appropriate Poisson distribution to the above data.
6. A biologist obtained a sample of number of eggs in the unopened flower heads of the black
Knapweed by the Knapweed fly. The flower heads in which no eggs were laid were not
included in the sample. Fit a truncated Poisson distribution to the data.
No. of eggs per flower head 1 2 3 4 5 ≥6
No. of flower heads 96 32 9 7 1 0