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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