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,
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