Approximations to the Binomial & Poisson Distributions


Exercises for students
Solve the following problems on paper and check your answers using the above applet:

Given X ~ Bin (100, 0.1).
Calculate the exact value of P(15 <= X <= 16).
Use the Poisson distribution to approximate the value of P(15 <= X <= 16).

Given X ~ Bin (100, 0.5).
Calculate the exact value of P(50 <= X <= 51).
Use the Normal distribution to approximate the value of P(50 <= X <= 51).

Given X ~ Po (20).
Calculate the exact value of P(15 <= X <= 16).
Use the Normal distribution to approximate the value of P(15 <= X <= 16).



(a) When a print job is sent to a printer, the probability of the job being made to join a queue is 0.2 .
100 independent print jobs are sent to the printer. Find the probability of being made to join a queue on at least 10 but not more than 20 of the jobs.
(b) When a print job is sent to a printer, the probability of paper jamming is 0.01 .
When 100 independent print jobs are sent, find the probability of paper jamming fewer than 3 times.



Accidents occur on a stretch of road at an average rate of 1.5 per week .
During a 10-week period, find the probability of at least 10 but not more than 20 accidents occurring.





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