Question

When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. If 25 such discs are tested:

What is the probability that 20 are not defective?

A) 0.368
B) 0.528
C) 0.491
D) 0.672

Answer 1

The probability that 20 out of 25 circuit boards are not defective is calculated using the binomial probability formula with n=25, k=20, and the success probability p=0.95 (since the defect rate is 5%, the non-defect rate is 95%).

Step-by-step explanation:

To find the probability that exactly 20 out of 25 circuit boards are not defective when the long-run percentage of defectives is 5%, we can use the binomial probability formula. The binomial probability formula in general is:

P(X=k) = C(n, k) * p^k * (1-p)^(n-k)

where:

C(n, k) is the combination of n items taken k at a time

P(X=k) is the probability of k successes in n trials

p is the probability of success on an individual trial

(1-p) is the probability of failure on an individual trial

For this problem:

n = 25 (number of trials)

k = 20 (number of non-defective boards needed)

p = 0.95 (probability of a non-defective board, which is 1 - 0.05)

Using the formula, we get:

P(X=20) = C(25, 20) * 0.95^20 * (1-0.95)^(25-20)

Performing the calculations, we arrive at one of the provided options as the answer.