Question

Bender Electronics buys keyboards for its computers from another company. The keyboards are received in shipments of 100 boxes, each box containing 20 keyboards. The quality control department at Bender Electronics first randomly selects one box from each shipment and then randomly selects 5 key boards from that box. The shipment is accepted if not more than 1 of the 5 keyboards is defective. The quality control inspector at Bender Electronics selected a box from a recently received shipment of keyboards. Unknown to the inspector, this box contains 6 defective keyboards.
Round your answers to four decimal places.
a. What is the probability that this shipment will be accepted?
P(shipment accepted)=
b. What is the probability that this shipment will not be accepted?
P(shipment not accepted)=

Answer 1

Answer:

(a) 0.5282

(b) 0.4718

Step-by-step explanation:

It is provided that the shipment is accepted if not more than 1 of the 5 keyboards is defective. That is for the shipment to be acceptable there should be at most 1 defective .

It is also provided that the box selected has 6 defective keyboards.

So, the probability of selecting a defective keyboard is, p = 6/20.

Let X = number of defective keyboards.

The random variable X follows a binomial distribution with parameters n = 6 and p = 6/20.

(a)

Compute the probability that this shipment will be accepted as follows:

$P(X\leq 1)=P(X=0)+P(X=1)$

               $=[{5\choose 0}(\frac{6}{20})^{0}(1-\frac{6}{20})^{5}]+[{5\choose 1}(\frac{6}{20})^{1}(1-\frac{6}{20})^{4}]\\\\=0.16807+0.36015\\\\=0.52822\\\\\approx 0.5282$

Thus, the probability that this shipment will be accepted is 0.5282.

(b)

Compute the probability that this shipment will not be accepted as follows:

P (shipment not accepted) = 1 - P(shipment accepted)

                                          = 1 - 0.5282

                                          = 0.4718

Thus, the probability that this shipment will not be accepted is 0.4718.