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 heart transplants performed per day in a country is about eight. Find the probability that the number of heart transplants performed on any given day is​ (a) exactly six​, ​(b) at least seven​, and​ (c) no more than four. ​(a) ​P(6​)equals nothing ​(Round to three decimal places as​ needed.)

Answer 1

X ~ Poi ( )

Where = 8

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

a)

P(6) = e^-8 * 8⁶ / 6!

= 0.122

b)

P(X >= 7) = 1 - P(X <= 6)

= 1 - POISSON.DIST ( x , Mean , cumulative) (Using EXCEL)

= 1 - POISSON.DIST ( 6 , 8 , TRUE)

= 1 - 0.3134

= 0.687

c)

P(X <= 4) = POISSON.DIST ( x , Mean , cumulative) (Using EXCEL)

= POISSON.DIST ( 4 , 8 , TRUE)

= 0.100