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

$P=0.3079$

Step-by-step explanation:

We can use the binomial formula to solve this problem.

$P(X=x)=\frac{n!}{x!(n-x)!}*p^x(1-p)^{n-x}$

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

$P(X=1)=\frac{25!}{1!(25-1)!}*0.02^x(1-0.98)^{25-1}$

$P(1)=0.3079$