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PAM 2100 INSTRUCTOR: SALAM ABDUS SAMPLE PRELIM QUESTIONS (PRELIM #1) In total there will be 8 problems and 20 multiple choice questions. 8 problems would be worth 60 points and the 20 multiple choice questions would be worth 40 points. The problems will be similar to the problems which you have solved in problem sets #1, #2 and #3. In what follows I have provided some sample questions for the problems. However, you should also review the problems in the problem sets thoroughly. I have also provided some samples for multiple choice questions. However, the practice problems that we have solved during the lectures are the best examples of the multiple choice questions which will show up in the prelim, and you should review them thoroughly. In the prelim you will be provided with copies of table A. I will also give you the equation for regression line. You can bring in any calculator. Problem 1 a) Below is a stemplot of home runs hit by major league teams during a month. What is the five- number summary of this data set? 2| 1 3| 5 4| 0 3 9 5| 1 2 3 4 6| 4 8 7| 5 Ans. 21 41.5 51.5 59 75 b) Consider a data set that includes every whole number from 1 to 51: 1, 2, 3, 4, 5, …. . ,50, 51 What is the five-number summary of this data set? Ans: 1 13 26 39 51 Problem 2 a) The median of x = 11 and the standard deviation of x = 7. The variable x is linearly transformed such that x new = 6x. What is the median of x new ? What is the standard deviation of x new ?

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Recall that multiplying each observation of a distribution by a positive number b multiplies both measures of center (mean, median) and spread (IQR, s) by b. The median of x new is (6)(11)= 66 and the standard deviation of x new is (6)(7)=42. b) The mean of x = 10 and the standard deviation of x = 4. The variable x is linearly transformed such that x new = a + bx. The mean of x new = 35 and standard deviation of x new = 12. Suppose that b is a positive number. What does a equal? What does b equal? See answer to the problem no. 2 of problem set #2 Problem 3 Chocolate bars produced by a certain machine are labeled with 8.0 oz. The distribution of the actual weights of these chocolate bars is normal with a mean of 8.1 oz. and a standard deviation of 0.1 oz. a) What proportion of chocolate bars weighs less than 8.0 oz? Round your value of z up to two
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