Final answer:
The probability that exactly 3 out of 9 randomly selected college graduates entered a profession related to their college major is 0.203 (b). The calculation is based on the binomial distribution formula.
Step-by-step explanation:
The student's question involves calculating the probability that 3 of the 9 randomly selected college graduates entered a profession related to their college major based on an initial survey of 300 graduates where 46% reported so. This can be modeled as a hypergeometric probability problem, but it resembles a binomial distribution since we are dealing with a large population and a small sample. The probability of exactly 3 out of 9 graduates reporting this can be calculated using the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
Where:
- n is the number of trials (9 graduates)
- k is the number of successes (3 graduates)
- p is the probability of success on any given trial (0.46)
Applying this to the binomial formula, we find:
P(3) = (9 choose 3) * 0.46^3 * (1-0.46)^6
After calculations, it can be determined that the closest answer provided by the options is 0.203, so choice b) 0.203 is correct.