QUESTION 1.

The life spans of a species of fruit fly have a bell-shaped distribution, with a mean of 35 days and a standard deviation of 5 days. (a) The life spans of three randomly selected fruit flies are 39 days, 30 days, and 49 days. Find the z-score that corresponds to each life span. Determine whether any of these life spans are unusual. (b) The life spans of three randomly selected fruit flies are 40 days, 45 days, and 50 days. Using the Empirical Rule, find the percentile that corresponds to each life span. (a) The z-score corresponding a life span of 39 days is. (Type an integer or a decimal rounded to two decimal places as needed.)The table shows population statistics for the ages of Best Actor and Best Supporting Actor winners at an awards ceremony. The distributions of the ages are approximately bellshaped. Compare the z-scores for the actors in the following situation. Best Actor Best Supporting Actor p. = 450 p. = 55.0 o' = 8.7 0' = 13 In a particular year, the Best Actor was 24 years old and the Best Supporting Actor was 59 years old. Determine the z-scores for each. Best Actor: 2 = Best Supporting Actor: 2 = (Round to two decimal places as needed.) Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a signicant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The table below shows the heights (in feet) and the number of stories of six notable buildings in a city. Height, x [ 775 | 619 519 508 491 474 El (a) x = 499 feet (b) x = 643 feet Stories, y | 53 | 47 46 42 37 35 (c) X = 310 feet (d) x = 736 feet Find the regression equation. y = x + ( ) (Round the slope to three decimal places as needed. Round the y-intercept to two decimal places as needed.) Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a signicant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below. 5 6 III (a) x = 2 hours (b) x = 2.5 hours (d) x = 4.5 hours Hours spent studying, x 1 2 2 | 3 Test score, y 39 45 52 | 48 63 72 (c) x = 12 hours Find the regression equation. = x+ ( ) (Round the slope to three decimal places as needed. Round the y-intercept to two decimal places as needed.) The accompanying data are the number of wins and the earned run averages (mean number of earned runs allowed per nine innings pitched) for eight baseball pitchers in a recent season. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. (a)x=5wins (b)x= 10 wins (c)x= 19 wins (d)x= 15 wins @ Click the icon to view the table of numbers of wins and earned run average. The equation of the regression line is 3? = x + (Round to two decimal places as needed.) X Wins and ERA Earned run Wins, x average, y 20 2.69 18 3.36 17 2.72 16 3.78 14 3.78 4.26 3.72 5.04The accompanying data are the length (in centimeters) and girths (in centimeters) of 12 harbor seals. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. (a)x=140cm (b)x=1720m (c)x=164cm (d)x=158cm @ Click the icon to view the table of lengths and girths. The equation of the regression line is )A/ = x + (Round to two decimal places as needed.) Lengths and Girths X Length, X Girth, y 138 106 168 130 153 117 145 105 159 124 159 120 123 104 136 103 154 120 149 111 147 108 147 109 Print DoneFind the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The caloric content and the sodium content (in milligrams) for 6 beef hot dogs are shown in the table below. Calories, x 160 180 130 120 90 190 (a) x = 170 calories (b) x = 100 calories Sodium, y 415 465 350 380 250 540 (c) x = 150 calories (d) x = 200 calories Find the regression equation. y = x +() (Round to three decimal places as needed.)The accompanying data are the caloric contents and the sugar contents (in grams) of 11 highber breakfast cereals. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. (a)x=160 cal (b)x=90 cal (c)x=175 cal (d)x=198 cal @ Click the icon to view the table of caloric and sugar contents. The equation of the regression line is ;= x + (Round to two decimal places as needed.) \fThe accompanying data are the shoe sizes and heights (in inches) of 14 men. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. (a)x=11.5 (b)x=8.0 (c)x=15.5 (d)x=10.0 @ Click the icon to view the table of shoe sizes and heights. The equation of the regression line is )7: x + (Round to two decimal places as needed.) X Shoe Sizes and Heights Shoe Size, x Height, y 8.5 66.5 9.0 69.0 9.0 68.0 9.5 70.0 10.0 70.5 10.0 72.5 10.5 71.0 10.5 69.5 11.0 71.5 11.0 72.0 11.0 72.5 12.0 73.5 12.0 74.0 12.5 73.5 Print DoneUse the data shown in the table that shows the number of bacteria present after a certain number of hours. Replace each y-value in the table with its logarithm, log y. Find the equation of the regression line for the transformed data. Then construct a scatterplot of (x, log y) and sketch the regression line with it. What do you notice? Number of hours, x 1 2 3 4 5 6 7 D Number of bacteria, y 141 230 398 670 1093 1825 3122 Find the equation of the regression line of the transformed data. log y = x + (Round to three decimal places as needed.) Use the data in the table below to complete parts (a) through (c). 5 7 8 12 13 18 20 42 :I 33 35 26 34 24 24 22 5 a Click the icon to View the steps for nding inuential points. (a) Construct a scatterplot of the data. Choose the correct graph below. C) A. O B. C) c. O D. A A A 12 y 0' 12 y Q 50$)!l Q 4o_y Q 7:. 0. . X) Q . 11 Q i Q ] 'f' ON 02 55 e 40 | '1 . 2' 2' ~ _. x 2| ._ x )- -12 D -12 L 0-! E' 0-1 '1' 0 4o 0 50 Use the data in the table below to complete parts (a) through (d). 38 33 40 | 46 22 20 25 ] 32 a Click the icon to view details on how to construct and interpret residual plots. (a) Find the equation of the regression line. g = x + ) (Round to three decimal places as needed.) Complete parts (a) through (c) using the following data. Row 1 2 3 4 5 5 5 6 6 | 6 7 I: Row 2 94 84 so 80 91 67 79 87 | 55 69 (a) Find the equation of the regression line for the given data, letting Row 1 represent the x-values and Row 2 the yvalues. Sketch a scatter plot of the data and draw the regression line