Question

The quality-control inspector of a production plant will reject a batch of automobile batteries if three or more defectives are found in a random sample of eleven batteries taken from the batch. Suppose the batch contains 7% defective batteries. What is the probability that the batch will be accepted?

Answer 1

p = 0.07

n = 11

P(X = x) = 11Cx * 0.07^x * (1-0.07)^11-x

P(acceptable) = P(X < 3)

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

= 11C0 * 0.07⁰ * 0.93¹¹ + 11C1 * 0.07¹ * 0.93¹⁰ + 11C2 * 0.07² * 0.93⁹

= 0.9630

Answer 2

SOLUTION :

p (defective) = 7% = 0.07

q(not defective) = 1 - 0.07 = 0.93 

Random sample size, n = 11

Now,

P(accept the batch) 

= P(defectives < 3)

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

= 11C0 p^0 q^11 + 11C1 p^1 q^10 + 11C2 p^2 q^9

=  1 * 1 * 0.93^11 + 11 * 0.07^1 * 0.93^10 + 55 * 0.07^2 * 0.93^9

= 0.9630 

So, probability that the batch will be selected is 0.963 (96.3%) (ANSWER).