Trowbridge Manufacturing produces cases for personal compute

Trowbridge Manufacturing produces cases for personal computers and other electronic equipment. The quality control inspector for this company believes that a particular process is out of control. Normally, only 5% of all cases are deemed defective due to discolorations. If 6 such cases are sampled, what is the probability that there will be 0 defective cases if the process is operating correctly? What is the probability thta there will be exactly 1 defective case?

Solution

here probability of defective cases= .05 and n=6

number of non defective cases = n = 6

=> P(x = 0) = 0.95^6 = 0.7351

the probability that there will be exactly 1 defective case

, x = 1 and

P(x = 1) = 6C1(0.05)^(0.95)^5 = 0.2321