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Unformatted text preview: Practice Midterm Exam and Solutions Statistics 371 Fall 2011 Professor Wardrop 1. Alicia will select a student a random from her biology class. You are given the follow ing facts about the students in her class. • Twenty percent are females and ju niors. • Fifteen percent are males and juniors. • Twenty¡ve percent are females and not juniors. Use this information to calculate the fol lowing probabilities. The student Alicia se lects is: (a) A junior. (b) A junior or a female. (Remember: Or means and/or.) (c) A male. 2. Kalinda will select a student a random from her criminal justice class. You are given the following facts about the students in her class. • Ten percent are females and veterans (military service). • Fifty percent are males. • Seventy percent are not veterans. Use this information to calculate the fol lowing probabilities. The student Kalinda selects is: (a) A veteran. (b) A veteran or a female. (Remember: Or means and/or.) (c) A female and not a veteran. 3. The 1,000 students at a small state univer sity are classi¡ed according to two features. Partial results are in the table below. Year Sex 1 2 3 4 T o t a l Female 190 140 120 150 600 Male 80 100 90 130 400 Total 270 240 210 280 1000 Consider the Chance Mechanism of select ing one student at random from the popula tion of 1,000 students. De¡ne the following events: • A : The student selected is in year 1. • B : The student selected is in year 3 or year 4. • C : The student selected is female, Use this information to obtain the follow ing probabilities. (a) P ( A or C ) . (b) P ( BC c ) . (c) P ([ A or B ] c ) . 4. The 1,000 students at a small state univer sity are classi¡ed according to three fea tures. Partial results are in the table below. Code Resident? 1 2 3 4 T o t a l Yes 260 150 160 130 700 No 140 100 40 20 300 Total 400 250 200 150 1000 The code is: • 1: Female Natural Science Major 1 • 2: Male Natural Science Major • 3: Female Social Science Major • 4: Male Social Science Major The Chance Mechanism is that one stu dent is selected at random from the popula tion of 1000 students. De¡ne the following events. • A: The selected student is a resident. • B: The selected student is female. • C: The selected student is a natural science major. Calculate the following probabilities. (a) P ( A ) . (b) P ( C ) (c) P ( AC ) (d) P ([ A or B ] c ) 5. Consider a sample space with three mem bers: 1, 2 and 3. We are given: P (1) = . 2 ,P (2) = 0 . 3 ,P (3) = 0 . 5 . Assume that we have i.i.d. trials. (a) Calculate P ( X 1 = X 2 ) . (b) Calculate P ( X 1 + X 2 + X 3 = 8) . 6. Consider a sample space with four mem bers: 0, 1, 3 and 5, with probabilities 0.1, 0.2, 0.3 and 0.4, respectively. Thus, this is not the equally likely case. Assume i.i.d....
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This note was uploaded on 12/10/2011 for the course STATS 371 taught by Professor Hanlon during the Fall '11 term at University of Wisconsin.
 Fall '11
 hanlon
 Statistics

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