A stationary store has decided to accept a large shipment of ball-point pens if an inspection of 16 randomly selected pens yields no more than two defective pens. (a) Find the probability that this shipment is accepted if 5% of the total shipment is defective. (Use 3 decimal places.)

(b) Find the probability that this shipment is not accepted if 20% of the total shipment is defective. (Use 3 decimal places.)

(a) The probability that the shipment is accepted if 5% of the total shipment is defective is 0.957.

(b) The probability that the shipment is not accepted if 20% of the total shipment is defective is 0.648.

Step-by-step explanation:

Let X = Number of defective pens.

The random variable X follows a binomial distribution with parameters n (sample size) = 16 and P (Success) = p.

The probability function of a Binomial distribution is:

; x = 0, 1, 2, 3...

It is provided that the shipment is accepted if there are no more than 2 defective pens in the lot.

(a)

The probability of defective pens in the shipment is, p = 0.05.

The probability that this shipment is accepted is:

P (X ≤ 2) = P (X = 0) + P (X = 1) + P (X = 2)

Thus, the probability that the shipment is accepted if 5% of the total shipment is defective is 0.957.

(b)

The probability of defective pens in the shipment is, p = 0.20.

The probability that this shipment is not accepted is:

P (X > 2) = 1 - P (X ≤ 2)

              = 1 - [P (X = 0) + P (X = 1) + P (X = 2)]

Thus, the probability that the shipment is not accepted if 20% of the total shipment is defective is 0.648.

ian gonna lie that is way to much