Question

Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities. The mean number of births per minute in a country in a recent year was about seven. Find the probability that the number of births in any given minute is (a) exactly six, (b) at least six, and (c) more than six. (a) P(exactly six)equals nothing (Round to four decimal places as needed.)

Answer #1

Solution :

Given that ,

mean = = 7

Using Poisson probability formula,

P(X = x) = (e^{-}
*
^{x} ) / x!

(a)

P(X = 6) = (e^{-7} * 7^{6)} / 6! = 0.1490

Probability = 0.1490

(b)

P(X 6) = 1 - P(X < 6) = 0.6993

Probability = 0.6993

(c)

P(X > 6) = 1 - P(X 6) = 0.5503

Probability = 0.5503

No any events are unusual .

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