Question

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 15% of the total shipment is defective. (Use 3 decimal places.)

Answer 1

X ~ binomial (n,p)

Binomial probability distribution is

P(X) = ⁿC_x p^x (1-p)^n-x

a)

n = 16 , p = 0.05

We have to calculate P(Shipment accepted) = P(X <= 2) = ?

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

= ¹⁶C₀ 0.05⁰ 0.95¹⁶ + ¹⁶C₁ 0.05¹ 0.95¹⁵ +¹⁶C₂ 0.05² 0.95¹⁴

= 0.957

b)

n = 16 , p = 0.15

We have to calculate P(shipment not accepted) = P (X > 2) = ?

P( X > 2) = 1 - P( X <= 2)

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

= 1 - [ ¹⁶C₀ 0.15⁰ 0.85¹⁶ + ¹⁶C₁ 0.15¹ 0.85¹⁵ + ¹⁶C₂ 0.15² 0.85¹⁴ ]

= 1 - 0.5614

= 0.439