Aquality control engineer tests the quality of produced computers. suppose that 5% of computers have defects, and defects occur independently of each other. a. what is the expected number of defective computers in a shipment of twenty? 1 b. find the probability of exactly 3 defective computers in a shipment of twenty.

Binomial distribution can be used because the situation satisfies all the following conditions:1. Number of trials is known and remains constant (n=20)2. Each trial is Bernoulli (i.e. exactly two possible outcomes) (defective/normal)3. Probability is known and remains constant throughout the trials (0.05)4. All trials are random and independent of the othersThe number of successes(defects), x, is then given bywhere
For n=20, p=0.05,
the mean number of defects is np=20*0.05=1






probability of exactly 3 defects in a sample of 20 is 0.05958