Question

A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures.​ Historically, the failure rate for LED light bulbs that the company manufactures is 11​%. Suppose a random sample of 10% LED light bulbs is selected.

a. What is the probability that none of the LED light bulbs are defective?

b. What is the probability that exactly 1 of the LED light bulbs is defective?

c. What is the probability that 3 or fewer of the LED light bulbs are defective?

d. What is the probability that 4 or more of the LED light bulbs are defective?

Answer 1

Solution:

Given that p = 0.11, n = 10
P(X) = C(10, X) (0.15)^X (1-0.15)^10-X
a) P(X = 0) = C(10, 0) (0.11)^0 (1-0.11)^10-0
= 0.3118
b) P(X = 1) = C(10, 1) (0.11)^1 (1-0.11)^10-1
= 0.3853
c) P(X = 3) = C(10, 3) (0.11)^3 (1-0.11)^10-3
= 0.0706
d) P(X = 4) = C(10, 4) (0.11)^4 (1-0.11)^10-4
= 0.0153