Before computers, the calculation of binomial probabilities was quite difficult for large n and small p. There is an approximation to the binomial probabilities in this situation by using the Poisson distribution.
statistics
Description
Before
computers, the calculation of binomial probabilities was quite difficult for
large n and small p. There is an approximation to the binomial probabilities in
this situation by using the Poisson distribution. If cases when n ≥ 100 and np
≤ 10 (that is, the probability is 10% or less), the following formula
approximates the binomial probability:
P(Y =y) = e-np(np)y/y!
Use this
approximation to calculate the following binomial probabilities: The National Safety Council data shows that the
lifetime probabilities for a U.S. resident dying in a relatively common event,
such as a motor-vehicle accident 1 in 84. Use the approximation to determine
the probability that, of 200 randomly selected deaths in the United States,
