Suppose a shipment of 500 machine parts contains 62 defective and 438 non-defective machine parts. From the shipment you take a random sample of 25. You are interested in the number of defective machine parts out of 25 trials and corresponding probabilities.

When sampling with replacement (binomial), determine the probability of obtaining each number of defective machine parts.

I am trying to calculate the probability of getting a defective machine part.

Defective parts of out 500: 62/500=12.4%
Would the defective parts out of the 25 trials be: 25*.124=3.1

I am on the right track?? Any help or guidance would be greatly appreciated!

Yes, you are on the right track! To calculate the probability of obtaining a specific number of defective machine parts out of 25 trials when sampling with replacement (which follows a binomial distribution), you need to determine the probability of getting that specific number of defective machine parts in each trial.

To calculate the probability, you can use the formula for the binomial probability:

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

Where:
- P(X=k) is the probability of getting exactly k successes (defective machine parts in this case),
- n is the number of trials (25 in your case),
- k is the number of successes (defective machine parts in this case),
- p is the probability of success in a single trial (the proportion of defective machine parts in the shipment).

Based on your information, the proportion of defective machine parts in the shipment is 62/500 = 0.124.

Let's calculate the probability for each number of defective machine parts out of 25 trials:

For k = 0 (no defective parts):
P(X=0) = C(25, 0) * 0.124^0 * (1-0.124)^(25-0)

For k = 1:
P(X=1) = C(25, 1) * 0.124^1 * (1-0.124)^(25-1)

And so on, until k = 25.

Note that C(n, k) represents the binomial coefficient and can be calculated using the formula:

C(n,k) = n! / (k!(n-k)!)

Once you calculate the probabilities for each number of defective machine parts, you will have the probability distribution for the number of defective machine parts out of 25 trials.