Early in august, an undergraduate college discovers that it can

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1) Early in August, an undergraduate college discovers that it can accommodate a few extra students. Enrolling those additional students would provide a substantial increase in revenue without increasing the operating costs of the college; that is, no new classes would have to be added. From past experience, the college knows that the frequency of enrolment given admission for all students is 40%.
a. what is the probability that at most 6 students will enroll if the college offers admission to 10 more students?
b. What is the probability that more than 12 will actually enroll if admission is offered to 20 students?
c. If the college would like to add 10 more students, how many admissions should they send out to expect 10 new enrollments?
d. What is the probability that exactly 10 more students will enroll if they send out the number of admissions from part c?
e. If the frequency of enrollment given admission was 70%, what is the probability that at least 12 out of 15 students will actually enroll?