# Normal and binomial distributions

A college would like to have an entering class of 1200 students. Because not all students who are offered admission accept, the college admits more than 1200 students. Past experience shows that about 70% of the students admitted will accept. The college decides to admit 1500 students. Assuming that students make their decisions independently, the number who accept has the B(1500, 0.7) distribution. If this number is less than 1200, the college will admit students from its waiting list.

1) The college does not want more than 1200 students. What is the probability that more than 1200 will accept?

2) If the college decides to increase the number of admission offers to 1700, what is the probability that more than 1200 will accept?

The scores of high school seniors on the ACT exam had a mean = 20.8 and standard deviation = 4.8. the distribution of scores is only roughly normal.

1) Take an SRS of 25 students who took the test. What are the mean and standard deviation of the sample mean score of these 25 students?

2) What is the approximate probability that the mean score of these students is 23 or higher?

3) What is the approximate probability that a single student randomly chosen from all those taking the test, scores 23 or higher?

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Please see the attached Word document for the solutions to these exercises.

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