Answer:
a) 0.00613 b) 0.113 c) 0.821, 0.804 d) 0.99997
Step-by-step explanation:
Cumulative Poisson probability=∑(e^-μ) (μ^x) / k!
μ: mean=20
x: max number of successes
k: number of success from 1 to x
e= 2.71828
In this question use poisson distribtuion calculator
a) x≤13
(e^-20) (20^13) / 1! + (e^-20) (20^13) / 2! + ........+ (e^-20) (20^13) / 13!
probability= 0.00613
b) x>25
probability= 1- P(X≤25,20)
= 0.113
c) probability( 13≤x≤25)= P(X≤25,20)-P(X≤13,20)
0.88728 - 0.06613
= 0.821
probability( 13<x<25)= P(X<25,20)- P(X<13,20)
= 0.84323-0.03901
= 0.804
d) In poisson distribution, variance = mean
So, here x=40
P(X<40) = 0.99997
