f05_31_final_section3

# f05_31_final_section3 - STAT31 Final Exam Fall 2005 Name...

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Page 1 STAT31 Final Exam Fall 2005 December 17, 2005 N a m e : P I D : S e c t i o n # : Instructions: Fill in the above information. Bubble-in your name, correct PID and sign the honor pledge on the bubble sheet. Both of the bubble sheet and the question set will be collected. Each question has only one correct choice (decimals may need rounding). Use "number 2" pencil only - do not use ink - fill bubble completely. No notes or remarks are accepted - do not tear or fold the bubble sheet. Choice #5 is NEVER a correct answer. A grade of zero will be assigned for the entire exam if the bubble sheet is not filled out according to the above instructions. There are 35 questions. Each question is worth 1 point. The exam time is from 8:00AM to 10:00AM. 1. A soft-drink machine can be regulated so that it discharges an average of µ ounces per cup. If the ounces of fill are normally distributed with a standard deviation of 0.4 oz. what value should µ be set at so that 6-oz. cups will overflow only 1.5% of the time? A) 5.13 B) 6.87 C) 5.18 D) 6.00 2. The following quantities are available from a dataset with two variables X and Y : 15, 2, 3. XY XSS == = In addition, the intercept and slope of the regression line are 10, .6. ab What are the correlation r and Y ? A) -0.4; 1. B) -0.9; 19 C) -0.4; 19 D) -0.9; 1

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Page 2 3. If a student got A in Midterm I, she has 0.8 chance of getting A as the final grade; if she didn't get A in Midterm I, the chance of getting A as the final grade is 0.2. Suppose 1/5 of the students got A in Midterm I. If Sam did not get A as his final grade in this class, what's the probability that he got A in Midterm I? A) 4/5 B) 1/2 C) 1/17 D) 1/5 4. We roll a pair of standard fair dice and observe the total number of dots on the top faces. Our sample space is S={2,3,4,5,6,7,8,9,10,11,12}. What's the probability that the total number of dots is more than 8? A) 11/12 B) 5/18 C) 1/3 D) 5/12 5. A Tar Heel basketball player makes 80% of all his free throw attempts. During each practice he is going to shot 4 free throws. As a student of STAT 31, you are interested in finding out the probability for him to hit more than half free throws during the practice. Entry is P(X=k) where X is binomial with n=4 and p=0.2 k 0 1 2 3 4 P(X=k) 0.4096 0.4096 0.1536 0.0256 0.0016 Utilizing the above binomial table, that probability is A) 0.9728 B) 0.8192 C) 0.4096 D) 0.0272
Page 3 6. A study tries to understand how children grow. The data were obtained by measuring the heights of 161 children and their corresponding ages. Their average age is 23.5 months, average height is 79.85 centimeters and the correlation between height and age is 0.9. One can obtain a least-squares regression line as Height=64.932+0.6348*Age. What will be the slope of the regression line if we try to infer a child's age from her height by setting Height to be the explanatory variable? A) 1.2760. B) -0.6348. C) 1.5577. D) 1.5753. 7. A stack of four cards contains two red cards and two black cards. I select two cards, one at a time, and do not replace the first card selected before selecting the second card.

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f05_31_final_section3 - STAT31 Final Exam Fall 2005 Name...

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