Question

A College would like to have 1050 freshmen. This college cannot accommodate more than 1060. Assume that each applicant accepts with probability 0.6 and that the acceptances can be modeled by Bernoulli trials. If the college accepts 1700, what is the probability that it will have too many acceptances?

Answer 1

To find the probability of the college having too many acceptances, we use the binomial distribution to calculate the probability of having more than 1060 acceptances out of 1700 applications with a 0.6 acceptance rate. The probability is approximately 0.015 or 1.5%.

Step-by-step explanation:

To find the probability that the college will have too many acceptances, we need to calculate the probability of having more than 1060 acceptances out of 1700 applications. Since the acceptances can be modeled by Bernoulli trials, we can use the binomial distribution to calculate this probability.

The probability of a success (an applicant accepting) is 0.6, and the number of trials is 1700. We want to find the probability of having more than 1060 successes.

Using a binomial distribution calculator or software, we can calculate that the probability of having more than 1060 successes out of 1700 trials with a success probability of 0.6 is approximately 0.015.

Therefore, the probability that the college will have too many acceptances is approximately 0.015 or 1.5%.