Question

A machine has a 5% scrap rte. You produce 40 parts and want to know the exact probability 2 are defective.

a) Hypergeometric
b) Binomial
c) Negative binomial
d) Poisson
e) Normal

Answer 1

To find the probability using the binomial distribution, you can use the formula: P(X=k) = (nCk) * p^k * q^(n-k), where n is the number of parts, k is the number of defective parts, p is the probability of a part being defective, and q is the probability of a part not being defective. In this case, the probability that exactly 2 parts are defective using the binomial distribution is 0.234.

Step-by-step explanation:

To find the probability using the binomial distribution, we can use the formula:

P(X=k) = (nCk) * p^k * q^(n-k), where n is the number of parts, k is the number of defective parts, p is the probability of a part being defective, and q is the probability of a part not being defective.

In this case, n = 40, k = 2, p = 0.05, and q = 0.95. Plugging these values into the formula:

P(X=2) = (40C2) * 0.05^2 * 0.95^38

Using the combination formula, (40C2) = 780, we can calculate the probability:

P(X=2) = 780 * 0.05^2 * 0.95^38 = 0.234

So, the probability that exactly 2 parts are defective using the binomial distribution is 0.234.