Question

A study was conducted to determine whether there were significant differences between college students admitted through special programs (such as retention incentive and guaranteed placement programs) and college students admitted through the regular admissions criteria. It was found that the graduation rate was 89.6% for the college students admitted through special programs. If 9 of the students from the special programs are randomly selected, find the probability that at least 8 of them graduated. prob= ........

Answer 1

To find the probability that at least 8 out of 9 students graduated, we can use the binomial distribution formula. The formula requires the number of students selected, the graduation rate for students admitted through special programs, and the desired number of successes. By substituting these values into the formula, we can find the probabilities.

Step-by-step explanation:

To find the probability that at least 8 out of 9 students graduated, we can use the binomial distribution formula.

The formula for the probability mass function of a binomial distribution is:

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

Where:

• P(X=k) is the probability of getting exactly k successes (in this case, the number of students who graduated)
• C(n, k) is the number of combinations of n objects taken k at a time
• p is the probability of success (graduating rate for students admitted through special programs)
• n is the number of trials (number of students selected)

In this case, n = 9, k >= 8, and p = 0.896 (graduation rate for students admitted through special programs).

We need to calculate the probabilities for k=8 and k=9, and sum them up:

P(X>=8) = P(X=8) + P(X=9)

Using the binomial distribution formula, we can substitute the values into the formula and calculate the probabilities.