Stats Practice Exams(1) - Some Practce Exams This documen±...

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Some Practice Exams This document contains problems from past midterm exams with solutions. These are MODEL solutions and alternative solutions may qualify. To best prepare for the coming exam , it is suggested that you try to first solve the problems WITHOUT looking at the solutions. ********************************************************************************** 1. A certain business school, which charges $50,000 for its MBA program, offers a select group of its new students the following deal at the beginning of school: “We will waive the entire tuition fee if you pay us $125,000 (if and) when you become a CEO for the first time”. Assume that each student in that group has a 0.2 probability of becoming CEO. Also assume that students can become a CEO independently of each other. There are 8 students in the select group. If all 8 students agree to take this deal, is the school likely to realize a profit ON THE AVERAGE? Explain. Solution: The random variable Y- “ the number of CEO’s in the underlying group” is a Binomial variable because each student can become a CEO independently of the others AND WITH EQUAL PROBABILITY. The expected number of students becoming a CEO is ( ) * 8*0.2 1.6 E Y n . The expected profit of the school is therefore 1.6*125,000=200,000. On the other hand the LOSS of the school in tuition fee is 8*50,000=400,000. Hence the school is expected to lose money. What kind of a Business School will offer such a deal?... **********************************************************************************
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2. Justin enrolled into two classes last quarter: BUS 007 and BUS 008. Grades in both classes were approximately normally distributed with the Following parameters: 12 , 78 , 8 , 75 008 008 007 007 . Justin got the same grade in both classes. Find the percentage of students who did better than Justin in BUS 008 , given that his grade in BUS 007 was the upper decile grade. Solution: In the normal distribution the upper decile is always 1.28 standard deviations above the mean. Therefore Justin’s (raw) grade in Bus 007 was 007 007 1.28* 75 1.28*8 85.24 . The standardized grade of this raw grade IN BUS 008 is 85.24 78 .6033 12 Z The percentage of students who did better than Justin in BUS 008 is given by 1 ( .6033) 1 0.726 .274 P Z ************************************************************************************ 3. The curve below represents the cumulative percentage polygon of a variable. Insert the missing signs or sentence <, =, >, or “impossible (to ascertain)” (one and only one) between the symbols following the polygon. (Copy the answer into you exam book). No explanation required.
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A B 0 0.3 1 X 1 3 3 1 2 / ) ( Q Me Me Q Q B A Q Me B A X Me
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