Question

4. In a tire manufacturing process, in every 1000 new tires, 8 are found to have manufacturing defects. For a passenger car, four newly manufactured tires are randomly selected and installed.

a. What is the probability that none of the tires have any manufacturing defects.

b. What is the probability that all four tires have manufacturing defects.

c. If 40 randomly selected tires are installed on 10 cars, four per car, what is the probability that at least 4 cars will have minimum one tire with manufacturing defects?

Answer 1

Probability that there is a manufacturing defect in a tire = 8/1000

= 0.008

(a) Probability that none of the four tires have any manufacturing defects = = 0.9684

(b) Probability that all four tires have manufacturing defects = = 4.096E-9

(c) Probability that minimum one tire has manufacturing defect for a randomly selected car = 1 - P(none of the four tires have any manufacturing defects) = 0.0316

The probability that atleast 4 out of 10 cars will have minimum one tire with manufacturing defects = P(X ≥ 4)

where X is a binomial random variable with n = 10, p = 0.0316

P(X ≥ 4) = 1 - P(X ≤ 3) = 1 - binomcdf (10, 0.0316, 3)

= 0.00018