Probability Calculation for Graduates' Full-Time Employment

What is the probability that 29% or less of a sample of 300 graduates have full-time employment?

Given that only 29% of the 300 graduates find full-time employment within one month of graduation, assuming the university's claim that 32% will have employment is true, how can we calculate the probability of 29% or less of the sample having full-time employment?

Calculation Method:

Using a statistical software or calculator, we can determine the probability as follows:

To find the probability that 29% or less of a sample of 300 graduates have full-time employment, we can utilize the binomial distribution. This distribution is suitable in this scenario due to the binary outcome (employed or not employed) and the large sample size.

Let's denote the probability of a graduate being employed as 'p'. As per the university's claim, p = 0.32. Our goal is to calculate the probability of observing 29% or fewer graduates employed, which translates to finding P(X ≤ 0.29 * 300), where X follows a binomial distribution with parameters n = 300 and p = 0.32.

To compute this probability, we can employ a binomial cumulative distribution function denoted as F(x; n, p), which signifies the probability of observing X ≤ x. In this instance, we aim to determine F(0.29 * 300; 300, 0.32).

By substituting the values into the cumulative distribution function, we can ascertain the result. The probability can be approximated as P(X ≤ 0.29 * 300) ≈ F(0.29 * 300; 300, 0.32).