Question

Suppose that a KSU professor says he bets that less than half of KSU students have jobs. You take a random of twenty KSU students and find that 16 of them have jobs. What is the probability that you would find exactly 16 out of twenty have jobs if the .50 conjectured by the professor was correct? What is the probability that you would find 16 or more have jobs? What will you say to the professor?

Answer 1

The probability of exactly 16 out of 20 KSU students having jobs under the professor's 50% conjecture can be calculated using the binomial probability formula. To determine the probability of finding 16 or more students with jobs, the individual probabilities from 16 to 20 must be summed. The results can help to discuss the validity of the professor's claim.

Step-by-step explanation:

To determine the probability that exactly 16 out of 20 KSU students have jobs if the professor's conjecture of a 50% proportion was correct, we use the binomial probability formula:

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

Where:

To determine the probability of finding 16 or more students with jobs, sum the probabilities for 16, 17, 18, 19, and 20 successes.

For this example, calculate P(X=16), then use similar calculations for P(X=17) to P(X=20) and sum those probabilities.

To address the professor, you could present the calculated probabilities and discuss if the results support or challenge their claim based on the findings.