Question

An automobile manufacturer produces production parts with 98% accuracy. What is the probability that in a production run of 25 parts, only 1 is found to be defective?

A. 0.3254
B. 0
C. 0.3965
D. 0.3079

Answer 1

Answer: Option D

`P=0.3079`

Explanation:

We can use the binomial formula to solve this problem.

`P(X=x)=(n!)/(x!(n-x)!)*p^x(1-p)^(n-x)`

Where p is the probability of success, n is the sample size and x is the number of successes expected.

Note that in this case

`p = 0.02` (probability that a part is defective)

`n = 25`

`x = 1`

Then we calculate the probability

`P(X=1)=(25!)/(1!(25-1)!)*0.02^x(1-0.98)^(25-1)`

`P(1)=0.3079`