Let X be a passion random variable with mean one that repres

Let X be a passion random variable with mean one that represents the number of on the outside of a new washing machine. Assuming independence, compute the probability that in a sample of machine the total number of is less than 13.

Solution

There is a mean of 10*1 = 10 flaws in 10 machines.

Note that P(fewer than x) = P(at most x - 1).          
          
Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    10      
x = our critical value of successes =    13      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   12   ) =    0.791556476
          
Which is also          
          
P(fewer than   13   ) =    0.791556476