1 1. The time X (minutes) for a lab assistant to prepare the equipment for a certain experiment is believed to have a uniform distribution with A = 20 and B = 30. a. Write the pdf of X and sketch its graph. b. What is the probability that preparation time exceeds 27 minutes? c. Find the preparation mean time, then calculate the probability that preparation is within 2 minutes of the mean time? d. For any a such that 20 < a < a + 2 < 30, what is the probability that preparation time is between a and a + 2 minutes? 2. Let X have a uniform distribution on the interval [a, b]. a. Obtain an expression for the (100p) th percentile. b. Compute E(X), V(X), and 2. c. For n a positive integer, compute E(Xn) 3. Let X be the temperature in let Y be the temperature in at which a certain chemical reaction takes place, and (so Y = 1.8X + 32). a. If the median of the X distribution is 2, show that 1.8 the Y distribution. + 32 is the median of b. How is the 90th percentile of the Y distribution related to the 90th percentile of the X distribution? Verify your conjecture. c. More generally, if Y = aX + b, how is any particular percentile of the Y distribution related to the corresponding percentile of the X distribution? 4. The distribution of resistance for resistors of a certain type is known to be normal, with 10% of all resistors having a resistance exceeding 10.634 ohms, and 5% having a resistance smaller than 9.7565 ohms. What are the mean value and standard deviation of the resistance distribution? 5. Suppose only 40% of all drivers in Florida regularly wear a seatbelt. A random sample of 500 drivers is selected. What is the probability that a. Between 170 and 220 (inclusive) of the drivers in the sample regularly wear a seatbelt? b. Fewer than 175 of those in the sample regularly wear a seatbelt? Assignment 2 Multiple Choice Identify the choice that best completes the statement or answers the question. 3,500 extra calories means 1 pound of excess weight, published in a newspaper's health section in 2005, featured a reader's question about having gained 10 pounds over the past year, and the health columnists' response: "Since it takes 3,500 calories over what your body needs to gain 1 pound of fat, an extra 100 calories every day can add 10 pounds in just one year." ____ 1. If the reported relationship between excess calories and weight gain is what scientists assume to hold universally, on average, then what notation should be used instead of ? a. b. c. s d. e. f. g. h. r Prices of a sample of generic drugs were regressed on the prices of the brand-name equivalents. The regression equation is Generic = -4.4 + 0.689 Brand Predictor Constant Brand Coef 4.37 0.68872 S = 22.87 SE Coef 16.11 0.08865 T 0.27 7.77 RSq = 78.0% P 0.790 0.000 RSq(adj) = 76.7% Predicted Values for New Observations New Obs 1 Fit 105.14 SE Fit 5.37 95.0% CI (93.82, 116.46) Values of Predictors for New Observations New Orbs Brand 159 1 ____ 2. Which of these is true about the confidence interval (C.I.)? a. For large samples and explanatory values not far from their mean, it is approximately . b. For large samples, and explanatory values not far from their mean, it is approximately . An annual state assessment test is a standards-based, criterion-referenced assessment used to measure a student's attainment of the academic standards while also determining the degree to which school programs enable students to attain proficiency of the standards. For a sample of schools, three relationships are considered: percentage passing versus school mean score, percentage passing versus percentage who participated (took the test) in each school, and percentage passing versus percentage of disadvantaged students in the school. In this exercise, you are to identify which one of the three reported regression results corresponds to each of the three scatterplots. 95.0% PI (55.58, 154.70) ____ 3. 95% confidence interval for on the right) for regression of % passing on disadvantaged (plot a. ( -0.78, -0.50) b. (0.17, 0.20) c. (0.30,+1.61) ____ 4. t statistic to test if right) = 0 for regression of % passing on disadvantaged (plot on the a. -9.05 b. +2.90 c. +27.90 Miles driven (in thousands) were regressed on year for a sample of used Ford Mustangs, and interval estimates requested for cars manufactured in the year 2000. The regression equation is Miles = 10453 - 5.20 Year Predictor Constant Year Coef 10453 5.2007 S = 8.629 New Obs 1 SE Coef 1256 0.6261 RSq = 64.5% Fit 51.93 SE Fit 4.31 95.0% CI (43.22, 60.65) T 8.32 8.31 P 0.000 0.000 RSq(adj) = 63.6% 95.0% PI (32.41, 71.46)X ____ 5. Interval estimates were requested for the mileage on a 2000 Ford Mustang. The output shows that 65 thousand miles driven is a. reasonable for an individual 2000 Ford Mustang b. reasonable for the mean mileage of all 2000 Ford Mustangs c. both (a) and (b) d. neither (a) nor (b)