1. 125 Points) Each manager of a Fortune 500 company was rated as being either a
ID: 2930438 • Letter: 1
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1. 125 Points) Each manager of a Fortune 500 company was rated as being either a good, fair, or poor manager by his/her boss. The manager's educational background was also noted. The data appear below. Educational Background Manager H.S. degree Ratin Good Fair Poor Total PhD Total Total MS 39 87 34 160 2 24 49 20 18 43 15 32 79 a. What is the probability that a manager does not have a BS? b. What is the probability that a manager is fair and does not have a BS? c. What is the probability that a manager is poor or has a H.S. degree? d. If the given manager is not fair, what is the probability that he has a MS degree? e. If the given manager is poo, what is the probability that he has a MS degree?Explanation / Answer
Question 1(A)
Probability that a manager doesn't have a BS degree = 1 - Probability that a manager have a BS degree
Pr(No BS Degree) = 1 - Pr( Have BS Degree)
Pr( Have BS Degree) = Total BS Degree Holder/ Total Students = (8 + 15 + 9 )/ 160 = 0.2
so,
Pr(No BS Degree) = 1 - Pr( Have BS Degree) = 1 - 0.2 = 0.8
(b) Pr(Manager is fair and Does not have BS) = Number of managaers who are fair and not have BS/ Total managers = (3 + 49 + 20)/ 160 = 0.45
(C) Pr( Mananager is poor or Manager have HS.) = NUmberof managers who are poor or have HS/ Total managers = (2 + 3 + 9 + 6 + 18 + 1)/ 160 = 0.24375
(D) Here now we have to find that the given manager is not fair, he has an MS degree
Pr(givenmanager is not fair, he has an MS degree) = Pr(Not fair and MS degree)/ Pr (Not fair)
= Total number of manager who are not fair and have MS Degree / Total number of managers having MS degree
SO Total number of manager who are not fair and have MS Degree = 24 + 6 = 30
Managers who are not fair= 39 + 34 = 73
Pr(givenmanager is not fair, he has an MS degree) = 30/73 = 0.411
(e) Pr(He has a MS Degree l Manager is poor) = Total number of MS degree manager who are poor/ Total number of poor manager = 6/34 = 0.1765
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