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under the standard normal curve2a) Find the area to the left of z=2.323a)The area to the right of z=0.494a) The area between z=-0.82 and z=2.11 is5) Find the z-score for which the area to its right is 0.09 Round the answer to two decimal places.6) A normal population has mean=8and standard deviation=s6(a) What proportion of the population is less than 22?(b) What is the probability that a randomly chosen value will be greater than 5?Round the answers to four decimal places.7)A normal population has mean=62and standard deviation=s17(a) What proportion of the population is greater than 103?(b) What is the probability that a randomly chosen value will be less than 79?8)A normal population has mean=39and standard deviations=10(a) What proportion of the population is between 17 and 28?(b) What is the probability that a randomly chosen value will be between 35 and 45?Round the answers to at least four decimal places.9) A normal population has mean =58and standard deviation s=9What is the 88th percentile of the population? Round the answer to at least one decimal place.10)Baby weights: The weight of male babies less than 2 months old in the United States is normally distributed with mean 12.4 pounds and standard deviation 5.2 pounds. Round to at least 2 decimal places(a) Find the 80th percentile of the baby weights.(b) Find the 17th percentile of the baby weights.(c) Find the first quartile of the baby weights.11)Fish story: According to a report by the U.S. Fish and Wildlife Service, the mean length of six-year-old rainbow trout in the river in Alaska is485 millimeters with a standard deviation of 45 millimeters. Assume these lengths are normally distributed.(a) What proportion of six-year-old rainbow trout are less than 456millimeters long?(b) What proportion of six-year-old rainbow trout are between 386 and 486 millimeters long?(c) Is it unusual for a six-year-old rainbow trout to be less than 388 millimeters long?Round the answers to at least four decimal places.12) How much do you study? A survey among freshmen at a certain university revealed that the number of hours spent studying the week before final exams was normally distributed with mean 28 and standard deviation 8Round the answer to at least four decimal places.(a) What proportion of students studied more than 39 hours?(b) What is the probability that a randomly selected student spent between 16 and 36 hours studying?(c) What proportion of students studied less than 36 hours?MathStatistics and Probability MATH 111

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