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[-/1 Points] DETAILS ILLOWSKYINTROSTAT1 7.1.064.HW. MY NOTES Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 141 minutes with a standard deviation of 12 minutes. Consider 49 of the races. Let X = the average of the 49 races. Part (a) Give the distribution of X. (Round your standard deviation to two decimal places.) X - N Enter an exact number, Part (b) Find the probability that the average of the sample will be between 139 and 144 minutes in these 49 marathons. (Round your answer to four decimal places.) Part (c) Find the 80th percentile for the average of these 49 marathons. (Round your answer to two decimal places.) |min Part (d) Find the median of the average running times. min[-/1 Points] DETAILS ILLOWSKYINTROSTAT1 7.1.062.HW. Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 236 feet and a standard deviation of 58 feet. We randomly sample 49 fly balls. Part (a) If X = average distance in feet for 40 fly balls. then give the distribution of X. Round your standard deviation to two decimal places. X - N 238 Part (b) What is the probability that the 40 balls traveled an average of less than 224 feet? (Round your answer to four decimal places.) Sketch the graph. Scale the horizontal axis for X Shade the region corresponding to the probability. O 220 230 240 250 260 O 220 230 240 250 260 O 220 230 240 250 260 O 220 230 240 250 260 Part (c) Find the 70th percentile of the distribution of the average of 40 fly balls. (Round your answer to two decimal places.) ftAccording to the Internal Revenue Service, the average length of time for an individual to complete (keep records for, learn, prepare, copy, assemble, and send) IRS Form 1040 is 10.66 hours (without any attached schedules). The distribution is unknown. Let us assume that the standard deviation is two hours. Suppose we randomly sample 36 taxpayers. Part (a) (@ Part (b) () Part (c) Give the distribution of X (Round your answers to two decimal places.) X - NY 10.66 ( Part (d) Find the probability that the 36 taxpayers took an average of more than 12 hours to finish their Form 1040s. (Round your answer to four decimal places.) ( Part (9) Would you be surprised if the 36 taxpayers finished their Form 1040s in an average of more than 12 hours? Explain why or why not in a complete sentence. No. because the probability is very close to 1. O Yes, because the probability is very close to 0.The percent of fat calories that a person consumes each day is normally distributed with a mean of about 34 and a standard deviation of about ten. Suppose that 25 individuals are randomly chosen. Let X = average percent of fat calories. (a) Give the distribution of X. (Round your standard deviation to two decimal places.) (b) For the group of 25, find the probability that the average percent of fat calories consumed is more than seven. (Round your answer to four decimal places.) Graph the situation and shade in the area to be determined. none none 0.20 0.20 0.15 0.15 0.10 0.10 0.05 0.05 ULL O 15 20 25 30 35 40 O 10 15 20 30 35 40 none 0.20 0.15 0.10 0.OS 10 15 20 25 30 35 15 20 X 25 30 35 40 (c) Find the first quartile for the average percent of fat calories. (Round your answer to two decimal places.) percent of fat calories[0.3/1 Points] DETAILS PREVIOUS ANSWERS ILLOWSKYINTROSTAT1 7.2.074.HW. MY NOTES ASK YOUR Suppose that the weight of open boxes of cereal in a home with children is uniformly distributed from one to three pounds with a mean of two pounds and standard deviation of 0.5774. We randomly survey 64 homes with children. Part (o] Part (b) Give the distribution of X. (Enter exact numbers as integers, fractions, or decimals.) X - 7 Y Part (c] Part (d) Give the distribution of EX. (Round your answers to two decimal places.) EX - NY ( Part (e] Find the probability that the total weight of open boxes is less than 130 pounds. (Round your answer to four decimal places.) Part of) Find the 65"h percentile for the total weight of open boxes of cereal (Round your answer to two decimal places.) Ib