a product is manufactured in batches of 120 and the overall

a product is manufactured in batches of 120 and the overall rate of defects is 5%. Estimate the probability that a randomly selected batch contains between 5 and 8 defects.

Solution

Note that P(between x1 and x2) = P(at most x2) - P(at most x1 - 1)          
          
Here,          
          
x1 =    5      
x2 =    8      
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    120      
p = the probability of a success =    0.05      
          
Then          
          
P(at most    4   ) =    0.278191271
P(at most    8   ) =    0.852593499
          
Thus,          
          
P(between x1 and x2) =    0.574402227   [ANSWER]