Question

The number of work-related injuries per month in a manufacturing plant is known to follow a Poisson distribution, with a mean of 3.5 work-related injuries a month.

a. Write the appropriate Poisson 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 two work-related injury occurs?.

Answer 1

SOLUTION-

NO OF WORK RELATED INJURIES ~ POISSON(3.5)

A.) THE PROBABILITY MASS FUNCTION FOR A POISSON DISTRIBUTION WITH PARAMETER IS,

P(X=x) =

B.) P( NO WORK RELATED INJURY)

= P(X=0)

=

= 0.0302

C.) P( ATLEAST TWO INJURIES OCCUR)

= P( X>=2)

= 1 - P(X<2)

= 1 - (P(X=0) + P(X=1))

= 1 -

= 1 - (0.0302 + 0.1057)

= 1 - 0.1359

= 0.8641

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