A machine that manufactures automobile parts produces defective parts 14% of the time. If 6

Question

A machine that manufactures automobile parts produces defective parts 14%

of the time. If 6

parts produced by this machine are randomly selected, what is the probability that fewer than 2

of the parts are defective?

Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places.

(If necessary, consult a list of formulas.)

Answer 1

We have a binomial distribution: A fixed number of "trials" with each trial having two possible outcomes (success/failure), and the probability of success is the same for each trial.

Probability of fewer than 2 is the probability of 0 or 1.

P(x=0) = 6C0 * 0.14^0*(1-0.14)^6 = 0.4046

P(x=1) = 6C1 * 0.14^1 * (1-0.14)^5 = 0.3952

P(x<2) = 0.4046 +0.3952 = 0.7998