Answer:
(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 <em>X</em> = Number of defective pens.
The random variable <em>X</em> follows a binomial distribution with parameters <em>n</em> (sample size) = 16 and P (Success) = <em>p</em>.
The probability function of a Binomial distribution is:
; <em>x</em> = 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, <em>p</em> = 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, <em>p</em> = 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.