between replacement periods? 6.80 The First-Year Class The admissions office of
ID: 3329443 • Letter: B
Question
between replacement periods? 6.80 The First-Year Class The admissions office of a small university is asked to accept deposits from a number of qualified prospective first-year students so that, with probability about 0.95, the size of the first year class will be less than or equal to 120. Suppose the applicants constitute a random sample from a population of applicants, 80% of whom would actually enter the first-year class if accepted a. How many deposits should the admissions counsel- lor accept? b. If applicants in the number determined in part a are accepted, what is the probability that the first-year class size will be less than 105? 681 No Shows. again An airline finds that 50Explanation / Answer
Q.6.80
Pr(Any accepted student will actually appear and enter the first year) = 0.80
Maximum number of student accepted = 120
Let say there are X if the number of students which must be asked to accept the deposits to make the probability of students entering in the first year equal or less than 120 shall be greater than 0.95
that means statistically,
Pr(x <= 120 ) >= 0.95
where expected number of first year student entering in the class = 0.8 X
standard deviation of the number of students entering in the class = sqrt( 0.8 * 0.2 * X) = 0.4 x
=> Z - value for p - value = 0.95 is
Z = 1.645
(120 - 0.8X)/ 0.4x = 1.645
120 - 0.8x = 0.658x
14,400 + 0.64x2 - 192x = 0.433x
14400 + 0.64 x2 - 192.433x = 0
x1 = 160.42 and x2 = 140.26
so x1 is invalid
so number of maximum student whose application must be accepted = 140.26 or 140
(b) so, let say that number of applicants accepted are 140
Expected number of admissions = 140 * 0.8 = 112
standard deviation of admission = sqrt (140 * 0.8 * 0.2) = 4.733
so Pr(X < 105; 112 ; 4.733) = ?
Z = (105 - 112)/ 4.733 = - 1.48
so Pr(Z < -1.48) = 0.0694
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