<p>Probability & Statistics – Final Exam Review</p><p>1. The state gas tax (in cents) for 25 states is given below.</p><p> a. Construct a frequency distribution table with 5 classes. b. Use this frequency distribution table to create a histogram for the data. c. Find the mean, standard deviation, 5-number summary and IQR d. Create a boxplot for the data. e. Which amount would correspond to the 75th percentile?</p><p>7.5 16 23.5 17 22 21.5 19 20 27.1 20 22 20.7 17</p><p>28 20 23 18.5 25.3 24 31 14.5 25.9 18 30 31.5</p><p>2. Use the following data to construct a boxplot and then test to see if there are any outliers:</p><p>89 47 164 296 30 215 138 78 48 39</p><p>3. A package contains 12 resistors, 3 of which are defective. If 4 are selected at random, find the probability of getting:</p><p> a. 0 defective resistors b. At least 1 defective resistor c. All defects</p><p>4. How can you tell the general shape of a distribution [symmetric or skewed] if all you know if the mean and median of the distribution?</p><p>5. An insurance company insures a person’s vehicle for $32,000 for an annual premium of $1,200. We will simplify things by considering the following two outcomes: If the company figures that the probability of the car being totaled is .0325 and the probability of paying $5000 for a minor accident is .1152, what will be the company’s expected profit?</p><p>6. Each month, an American household generates an average of 28 pounds of recyclables for garbage. Assume the standard deviation is 2 pounds. If a household is selected at random, find the probability of generating: a. Between 27 and 31 pounds per month b. More than 30.2 pounds per month</p><p>Assume the variable is normally distributed. </p><p>7. Define or describe the following : a. Inferential Statistics & Descriptive Statistics b. Data collection methods c. Rounding rule for reporting statistics d. Qualitative & Quantitative Variables [continuous & discrete too] 8. Answer the following questions involving correlation and regression:</p><p> a. The correlation coefficient r can be any value between _____ and _____. </p><p> b. When all points fall on the regression line, the value of the correlation coefficient would be r = _____. </p><p> c. When a correlation is weak, r is close to _____. </p><p> d. When a correlation is strong [and negative], r is close to _____. </p><p> e. What does the coefficient of determination [ ] tells us?</p><p> f. A statistical graph of two quantitative variables is called a ______. </p><p> g. Another name for the x-variable is the ______variable. </p><p> h. Another name for the y-variable is the ______variable. </p><p> i. What is the study of linear regression used for in the practice of statistics?</p><p>9. Find the weighted mean (GPA) of this student’s fall semester. </p><p>Course Credits Grade Points</p><p>English Composition 3 3.5</p><p>Calculus 4 2.8</p><p>Psychology 3 3.0</p><p>Sociology 3 4.0</p><p>10. Find the z-scores for the following tests and state which one the student did better on relative to his/her classmates. </p><p>Test A Score = 45 Mean = 48 S = 5</p><p>Test B Score = 80 Mean = 93 S = 10</p><p>11. Perform a linear regression analysis to predict sales from $ spent on advertising. </p><p>Month 1 2 3 4 5 6 7 8 9 10 11 12</p><p>Advertising $ 5.5 5.8 6 5.9 6.2 6.3 6.5 6.6 6.4 6.5 6.7 6.8 (1000s)</p><p>Sales 100 110 112 115 117 116 118 120 121 120 117 123 (1000s)</p>