In a certain town,5% of college students suffer from manic-depressive illness.If 300 of the students are selected at random and screened,what is the probability that no more than 20 of them suffer from manic-depressive illness?
A)0.907
B)0.363
C)0.113
D)0.093
E)0.637

Question

Quizplus · Accepted Answer

This problem can be approached using the binomial distribution formula, which calculates the probability of having exactly k successes (in this case, students suffering from manic-depressive illness) out of n trials (students selected), given the probability p of success on a single trial. The probability of no more than 20 students suffering from the illness involves summing the probabilities of having 0 to 20 students with the illness. However, calculating this directly can be cumbersome. A more practical approach, especially for large n, is to use a normal approximation to the binomial distribution or a binomial probability calculator. Given the provided options and the nature of the question, it's likely that such an approximation or computational tool was used to arrive at the answer. The correct choice, A, suggests that the probability of no more than 20 students suffering from the illness is approximately 0.907, indicating a high likelihood that fewer than 20 of the 300 randomly selected students would have manic-depressive illness, based on the 5% prevalence rate.

In a Certain Town,5% of College Students Suffer from Manic-Depressive