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.

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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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