Losttime accidents occur in a company at a mean rate of 08 p

Lost-time accidents occur in a company at a mean rate of 0.8 per day. What is the probability that the number of lost-time accidents occurring over a period of 9 days will be at least 3 ? Round your answer to four decimal places.

Solution

The mean per day is 0.8, so for 9 days, the mean is 0.8*9 = 7.2.

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    7.2      
          
x = our critical value of successes =    3      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   2   ) =    0.025473508
          
Thus, the probability of at least   3   successes is  
          
P(at least   3   ) =    0.974526492 = 0.9745 [answer]