A particular lake is known to be one of the best places to catch a certain type of fish. In this table, x = number of fish caught in a 6-hour period. The percentage data are the percentages of fishermen who caught x fish in a 6-hour period while fishing from shore. 4 or more /% 43% 35% 15% 6% 1% (a) Convert the percentages to probabilities and make a histogram of the probability distribution. (Select the correct graph.) 1. 0.5 0.4 8 0.3 0.2 01 0 2 3 4 or more O 0.5 0.4 * 0.3 0.2 01 0 2 3 4 or more O 0.5 0.4 0.3 P(X 0.2 3.1 3 4 or more * N O 0.5 0.4 0.3 P(X 0.2 0.1 4 or more(b) Find the probability that a fisherman selected at random fishing from shore catches one or more fish in a 6-hour period. (Enter a number. Round your answer to two decimal places.) (c) Find the probability that a fisherman selected at random fishing from shore catches two or more fish in a 6-hour period. (Enter a number. Round your answer to two decimal places.) (d) Compute u, the expected value of the number of fish caught per fisherman in a 6-hour period (round 4 or more to 4). (Enter a number. Round your answer to two decimal places.) u = fish 1. cont'd (e) Compute , the standard deviation of the number of fish caught per fisherman in a 6-hour period (round 4 or more to 4). (Enter a number. Round your answer to three decimal places.) 0 = fishkilograms). You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some calves to add to the Bar-S herd. How much should a healthy calf weigh? Let x be the age of the calf (in weeks), and let y be the weight of the calf (in * 1 47 11 16 26 36 100 150 200 Complete parts (a) through (e), given Ex = 95, Ey = 609, Ex2 = 2375, Ey? = 81,559, Exy = 13,777, and / = 0.997. (a) Make a scatter diagram of the data. (Select the correct graph.) CHOICE A CHOICE B CHOICE C 200 200 200 150 150 150 100 100 100- 50 50 50 X O 10 20 30 40 O 10 20 L X 30 40 O 10 20 L X CHOICE D 30 40 y 200 150 2. 100 50 O 10 20 30 40 Ex = (b) Verify the given sums Ex, Zy, Ex', Zy', Ex y, and the value of the sample correlation coefficient r. (For each answer, enter a number. Round your value for r to three decimal places.) Ey = [x2 = Ey? = Exy = r =X = (c) Find x, and y. Then find the equation of the least-squares line y = a + b x. (For each answer, enter a number. Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) V = V = (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. (Select the correct graph.) CHOICE A CHOICE B CHOICE C 200 200 200 150 150 150 100 100 100 50 50 50 O 10 20 30 40 O 10 20 30 40 O 10 20 30 CHOICE D 40 2. cont'd 200 150 100 50 10 20 30 40 places. Round your answers for the percentages to one decimal place.) (e) Find the value of the coefficient of determination . What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (For each answer, enter a number. Round your answer for / to three decimal 2 = explained = unexplained = % kg (f) The calves you want to buy are 20 weeks old. What does the least-squares line predict for a healthy weight (in kg)? (Enter a number. Round your answer to two decimal places.)