Question

# Find the indicated probabilities using the geometric​ distribution, the Poisson​ distribution, or the binomial distribution. Then...

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.)

Solution :

Given that ,

mean = = 7

Using Poisson probability formula,

P(X = x) = (e- * x ) / x!

(a)

P(X = 6) = (e-7 * 76) / 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 .