Question

Buchtal, a manufacturer of ceramic tiles, reports on average 4.1 job-related accidents per year. Accident categories include trip, fall, struck by equipment, transportation, and handling. The number of accidents is approximately Poisson. Please upload your work for all of the parts at the end. What is the probability that more than one accident occurs per year?

Answer 1

0.9155

Explanation:

As, the random variable X the number of accident follows the Poisson distribution so,

P(X=x)=(μ^x)(e^-μ)/x!

μ=average accident=4.1.

The probability that more than one accident occurs per year= P(X>1)=?

P(X>1)=1-P(X≤1)

P(X>1)=1-[P(X=0)+P(X=1)]

P(X=0)=(4.1^0)(e^-4.1)/0!

P(X=0)=0.016573/1

P(X=0)=0.016573

P(X=1)=(4.1^1)(e^-4.1)/1!

P(X=1)=(4.1)0.016573/1

P(X=1)=0.0679481

P(X>1)=1-[0.016573+0.0679481]

P(X>1)=1-0.084521

P(X>1)=0.915479

P(X>1)=0.9155

The probability that more than one accident occurs per year is 91.55%