Can someone please help me with this example, I do not understand it at all.

Binomial problems: Advanced
A machine that manufactures automobile parts is estimated to produce defective parts % of the time. If this estimate is correct, and parts produced by this machine are randomly selected, what is the probability that at most turn out to be defective? Round your answer to four decimal places.

Let me try this again:

Binomial problems: Advanced
The unemployment rate in a city is 14%. Find the probability that more than 2 out of 6 people from this city sampled at random are unemployed. Round your answer to four decimal places.

The easiest way to do this problem is to use a binomial probability table. If you do this, you will need to find P(3), P(4), P(5), and P(6). In the table, n = 6, p = .14, x = 3, 4, 5, 6 (for each one). Add all these probabilities together for the total probability.

I hope this will help.

To solve this problem, we can use the binomial probability formula:

P(X ≤ k) = Σ[i=0 to k] (nCi * p^i * (1-p)^(n-i))

Where:
- P(X ≤ k) is the probability that at most k parts turn out to be defective.
- n is the total number of parts selected.
- k is the desired number of defective parts.
- p is the probability of a part being defective (given as a decimal).
- nCi is the binomial coefficient, which represents the number of ways to choose i defective parts out of n parts.

In this case, we have:
- p = 0.08 (since the machine is estimated to produce defective parts 8% of the time)
- We want to find the probability that at most k defective parts are produced, so k is the desired number of defective parts.
- We are not given the total number of parts selected, so we will represent it as n.

To calculate the probability, we need to sum up the probabilities for all possible values of i (defective parts) from 0 to k.

Let's calculate the binomial probabilities for each i and sum them up to find P(X ≤ k).