Question

The number of work related injuries per month in a manufacturing plant is known to follow a poission with a mean of 2.5 work related injuries a month. A write the appropriate piossion probability function B what is the probability that in a given month, no work related injuries occur C what is the probability that in a given month,at least one work related injury occurs.

Answer 1

a)

As per Poisson's distribution function P(X = x) = λ^x * e^(-λ)/x!

b)

Here, λ = 2.5 and x = 0
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X = 0)
P(X = 0) = 2.5^0 * e^-2.5/0!
P(X = 0) = 0.0821
Ans: 0.0821

c)

Here, λ = 2.5 and x =1
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X >=1 ) = 1 - P(X <= 0).
P(X >=1) = 1 - (2.5^0 * e^-2.5/0!)
P(X > =1) = 1 - (0.0821)
P(X >=1) = 1 - 0.0821 = 0.9179