Answer the questions neatly and in order. Use complete sentences where appropriate. Show all work and/or computations. Submit your work as a single pdf file to Canvas/ICON. You may use the table in your book (pages 370 and 371) or you can use technology to calculate percentages for the Normal distribution. Here is Matt Bognar's app that will calculate percentages/areas under the normal curve for any z-score! https://homepage.divms.uiowa.edu/~mbognar/appletsormal.html Problem #1 The women's heptathlon in the Olympics consists of seven track and field events: the 200-m and 800-m runs, 100-m high hurdles, shot put, javelin, high jump, and long jump. In the 2000 Olympics, the best 800-m time, run by Gertrud Bacher of Italy, was 8 seconds faster than the mean. The winning long jump by the Russian Yelena Prokhorova was 60 centimeters longer than the mean. Bacher's winning 800-m time of 129 seconds was 8 seconds faster than the mean qualifying time of 137 seconds (the standard deviation of the qualifying times was 5 seconds). Prokhorova's winning long jump was 60cm longer than the average 6-m jump (Note: the standard deviation of the long jumps was 30 cm). Which performance is more outstanding (and hence deserves more points when computing their overall score)? Explain.Problem #2 Sixweekold babies consume a mean of u = 15 ounces of milk per day, with a standard deviation 0 of 2 ounces. Assume that the distribution of milk consumption for these babies is normally distributed. a) Sketch and label the distribution of milk consumption for sixweekold babies. Include both the data scale and the standard scale. b) Estimate the proportion of babies who consume more than 17 ounces of milk per day. Sketch, label, and shade a picture; use the 68-95-99] rule. 0) Calculate the z-score for a baby who consumes 12 ounces of milk per day. d) Use the Normal tables or technology (Matt's app) to compute the proportion of babies who consume more than 12 ounces per day. Sketch, label, and shade a picture to show your work. e) What amount of daily milk consumption would you consider to be unusually low for a six-weekold baby? ExplainlJustify your reasoning. Problem #3 The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152 pounds. Suppose that weights of all such animals can be described by N(u=1152, 0:84). Where appropriate: Sketch, label, shade a picture; find zscores; write a sentence; use the Normal tables or technology if needed. a) How many standard deviations from the mean is a steer weighing 1000 pounds? b) Find the percentile corresponding to a steer weighing 1250 lbs. Write a sentence interpreting your result. Hint: First find the z-score. c) What percent of steers weigh over 1150 lbs? d) What percent of steers weigh between 1100 and 1300 lbs? Hint: Sketch a picture of the area you are trying to find. Problem #4 Carbon monoxide (CO) emissions for a certain kind of car vary with mean 2.9 g/mi and standard deviation 0.4 g/mi. Assume the distribution of emissions can be modeled with a Normal distribution. a) Use the Normal tables or technology to find the percentage of this type of car with CO emissions between 2.5 glmi and 3.0 glmi. Hint: Sketch a picture of the area you are trying to find. b) Multiple samples of 80 of these cars are randomly selected and the mean is found for each sample. What is the mean of the sample means? 0) Multiple samples of 80 of these cars are randomly selected and the mean is found for each sample. What is the standard deviation of the sample means? Problem #5 a) A friend tells you about a recent study dealing with the number of years of teaching experience among current college professors. He remembers the mean but can't recall whether the standard deviation was 6 months, 6 years, or 16 years. Tell him which one it must have been and why. b) Suppose your Statistics professor reports test grades as zscores, and you got a score of 2 on an exam. Write a sentence or two explaining what that means. 0) Explain why a normal distribution cannot have a standard deviation of O