Question

A stationary store has decided to accept a large shipment of ball-point pens if an inspection of 17 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 15% of the total shipment is defective. (Use 3 decimal places.)

Answer 1

Solution:

( a )

n = 17

p = 0.05

binomial probability distribution

Formula:

P_{(k out of n )}= n!*p^k * q^n-k / k! *(n - k)

P( x 2 ) = 17!*0.05² * 0.95^17-2 / 2! *(17 - 2)+17!*0.05¹ * 0.95^17-1 / 1! *(17 - 1)+17!*0.05⁰ * 0.95^17-0 / 0! *(17 - 0)

= 0.1575+0.3741+0.4181

= 0.949

( b )

n = 17

p = 0.15

binomial probability distribution

Formula:

P_{(k out of n )}= n!*p^k * q^n-k / k! *(n - k)

P( x 2 ) = 17!*0.15² * 0.85^17-2 / 2! *(17 - 2)+17!*0.15¹ * 0.85^17-1 / 1! *(17 - 1)+17!*0.15⁰ * 0.85^17-0 / 0! *(17 - 0)

= 0.2673+0.1893+0.0631

= 0.519