Poisson Approximation to the Binomial Probability
Distribution:
We have already studied how the Poisson distribution can be used with intervals of time,
space, area, and so on. However, Poisson can also be used as a probability distribution
for “rare” events. The Poisson distribution will be a very good approximation to the
binomial distribution provided that the number of trials n is larger than or equal to 100
and λ = np is less than 10. As n gets larger and p gets smaller, the approximation
becomes better and better.
Consider the binomial distribution with
n = number of trials
r = number of successes
p = probability of success on each trial
If n > 100 and np < 10, then r has a binomial distribution that is approximated by a
Poisson distribution with λ = np.
***Now complete problems on text p. 301 – 307.