Question

A study was conducted to determine whether there were significant differences between medical students admitted through special programs (such as retention incentive and guaranteed placement programs) and medical students admitted through the regular admissions criteria. It was found that the graduation rate was 92.4% for the medical students admitted through special programs. Be sure to enter at least 4 digits of accuracy for this problem!

a. If 12 of the students from the special programs are randomly selected, find the probability that at least 11 of them graduated.
prob =

Answer 1

The probability that at least 11 out of 12 randomly selected medical students from special programs graduated is approximately 0.9771.

The probability calculation involves using the binomial probability distribution, as the outcome (graduation or non-graduation) is binary. Given that the graduation rate for students admitted through special programs is 92.4%, we can compute the probability of different graduation outcomes for a sample of 12 students.

To find the probability that at least 11 out of 12 students graduated, we sum the individual probabilities of having exactly 11 graduates and exactly 12 graduates. This is expressed as P(X≥11)=P(X=11)+P(X=12), where X is the number of students who graduated.

Using the binomial probability formula, this probability is calculated as approximately 0.9771. Therefore, there is a high likelihood (97.71%) that at least 11 out of the 12 randomly selected medical students from special programs graduated, indicating a strong success rate in the context of the study.