Final answer:
The random variable X represents the number of business majors in a random sample of nine students. The distribution of X is approximately a binomial distribution, and the mean (µ) can be calculated using n * p, where n is the sample size and p is the probability of success in each trial.
Step-by-step explanation:
The random variable X represents the number of business majors in a random sample of nine students, where there are 16 business majors and 7 non-business majors in the population. Therefore, X can take on values ranging from 0 (if there are no business majors in the sample) to 9 (if all students in the sample are business majors).
The distribution of X is approximately a binomial distribution, denoted as X~B(9, p), where p is the probability of selecting a business major in each trial. The mean (µ) of X is given by µ = n * p, where n is the sample size and p is the probability of success in each trial.
To find the standard deviation of X, you can use the formula σ = sqrt(n * p * (1 - p)), where σ is the standard deviation, n is the sample size, and p is the probability of success in each trial.
On average, you can expect around µ = 9 * (16/23) ≈ 6.26 out of the 9 students in the sample to be business majors.