Asked by CM
The first-year retention rate is the percentage of entering freshman at a given college who return to that same college for their sophomore year. Many colleges use the first-year retention rate as one measure of their quality. Suppose that the first-year retention rate at a given college is 75% (a typical number).
a. One dormitory suite holds six first-year students. What is the probability that at least four of those students return for their sophomore year?
b. Suppose that this college admits 500 new first-year students every year, and has had a retention rate of 75% for a long time. What is the mean number of students who return for their sophomore year? What is the standard deviation for this number?
c. What is the probability that, in a given year, no more than 350 first-year students return for their sophomore year?
d. Suppose that in a given year, 410 students return for their sophomore year. Is this unusually high? Explain your answer.
a. One dormitory suite holds six first-year students. What is the probability that at least four of those students return for their sophomore year?
b. Suppose that this college admits 500 new first-year students every year, and has had a retention rate of 75% for a long time. What is the mean number of students who return for their sophomore year? What is the standard deviation for this number?
c. What is the probability that, in a given year, no more than 350 first-year students return for their sophomore year?
d. Suppose that in a given year, 410 students return for their sophomore year. Is this unusually high? Explain your answer.
Answers
Answered by
CM
a) One dormitory suite holds 6 first year students. what is the probability that at least four of those students return for their sophomore year?
b) suppose that this college admits 500 new first-year students every year and has had a retention rate of 75% for a long time. what is the mean number of students who return for their sophomore year? what is the standard deviation for this number?
c)what is the probability that in a given year no more than 350 first year students return for their sophomore year?
d)Suppose that in a given year, 410 students return for their sophomore year. is this unusually high? explain your answer.
Please help, I really have no idea, this stuff confuses me.
b) suppose that this college admits 500 new first-year students every year and has had a retention rate of 75% for a long time. what is the mean number of students who return for their sophomore year? what is the standard deviation for this number?
c)what is the probability that in a given year no more than 350 first year students return for their sophomore year?
d)Suppose that in a given year, 410 students return for their sophomore year. is this unusually high? explain your answer.
Please help, I really have no idea, this stuff confuses me.
Answered by
economyst
For a) you could calculate directly, or you could use a poisson distribution function. Let me calculate directly.
The probability that exactly n return is 6-choose-n * .75^n * .25^(6-n)
P(all) = .75^6 = .1720
P(5) = 6*(.75^5)*.25 = .3540
P(4) = ((6*5)/2)*(.75^4)*(.25^2) = .2966
So P(6,5,or4)=.1720+.3540+.2966=.8226
b) the for a binominal, the:
SD = sqrt(n*p*q) = sqrt(500*.75*.25) = 9.68
So, the expected mean is .75*500 = 375 with a SD of 9.68
c) 350 is 25 from the mean or 25/9.68 = 2.58. Looking up this value in a standard normal distribution table is .9951 Ergo, the probability of no more than 350 is 0.0049 or 0.49%
d) take in from here, follow the same logic as in c)
The probability that exactly n return is 6-choose-n * .75^n * .25^(6-n)
P(all) = .75^6 = .1720
P(5) = 6*(.75^5)*.25 = .3540
P(4) = ((6*5)/2)*(.75^4)*(.25^2) = .2966
So P(6,5,or4)=.1720+.3540+.2966=.8226
b) the for a binominal, the:
SD = sqrt(n*p*q) = sqrt(500*.75*.25) = 9.68
So, the expected mean is .75*500 = 375 with a SD of 9.68
c) 350 is 25 from the mean or 25/9.68 = 2.58. Looking up this value in a standard normal distribution table is .9951 Ergo, the probability of no more than 350 is 0.0049 or 0.49%
d) take in from here, follow the same logic as in c)
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.