A large manufacturing plant has averaged 7 reportable accide

A large manufacturing plant has averaged 7 “reportable accident” per month. Suppose that accident counts over time follow a Poisson distribution with mean 7 per month.

(a)What is the probability of exactly 7 accidents in a month?

(b)What is the probability of at least one accident in a month?

Solution

a)

Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    7      
          
x = the number of successes =    7      
          
Thus, the probability is          
          
P (    7   ) =    0.14900278 [ANSWER]

b)

Note that

P(at least 1) = 1 - P(0)

Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    7      
          
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.000911882

Thus,

P(at least 1) = 0.999088118 [ANSWER]