Question

A stationary store has decided to accept a large shipment of ball-point pens if an inspection of 18 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.)

Answer 1

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

P[ Shipment is defective ] = 5% = 0.05

Lot is accepted if 2 or lesser pieces are defective

sample size, n = 18

P[ Lot is accepted ] = P[ X <= 2 ]

P[ X <= 2 ] = P[ X = 0 ] + P[ X = 1 ] + P[ X = 2 ]

This implies that

P[ X <= 2 ] = 0.3972 + 0.3763 + 0.1683=

P[ X <= 2 ] = 0.9419

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

P[ Shipment is defective ] = 20% = 0.2

Lot is accepted if 2 or lesser pieces are defective

sample size, n = 18

P[ Shipment is rejected ] = P[ X > 2 ] = 1 - P[ X <= 2 ]

P[ X <= 2 ] = 0.018 + 0.0811 + 0.1723

P[ X <= 2 ] = 0.2713

P[ X > 2 ] = 1 - P[ X <= 2 ]

P[ X > 2 ] = 1 - 0.2713

P[ X > 2 ] = 0.7287