Its 13 on the bottom. Continued on the next page. Section 6.5The Central Limit Theorem329(b) What is the probability that 20 cars chosen at random will have a meanload weight x of less than 74.5 tons of coal?(c) Interpretation Suppose the weight of coal in one car was less than74.5 tons. Would that fact make you suspect that the loader had slippedout of adjustment? Suppose the weight of coal in 20 cars selected at ran-dom had an average x of less than 74.5 tons. Would that fact make yoususpect that the loader had slipped out of adjustment? Why?Vital Statistics: Heights of Men The heights of 18-year-old men are ap-proximately normally distributed, with mean 68 inches and standard devia-tion 3 inches (based on information from Statistical Abstract of the UnitedStates, 112th edition).(a) What is the probability that an 18-year-old man selected at random isbetween 67 and 69 inches tall?(b) If a random sample of nine 18-year-old men is selected, what is theprobability that the mean height x is between 67 and 69 inches?(c) Interpretation Compare your answers to parts (a) and (b). Is the prob-ability in part (b) much higher? Why would you expect this?Medical: Blood Glucose Let x be a random variable that represents the levelof glucose in the blood (milligrams per deciliter of blood) after a 12-hour fast.Assume that for people under 50 years old, x has a distribution that is approx-imately normal, with mean u(based on information from Diagnostic Tests with Nursing Applications,edited by S. Loeb, Springhouse). A test result x

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Description: Its 13 on the bottom. Continued on the next page. Section 6.5The Central Limit Theorem329(b) What is the probability that 20 cars chosen at random will have a meanload weight x of less than 74.5 tons of coal?(c) Interpretation Suppose the weight of c

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Its 13 on the bottom. Continued on the next page. Section 6.5The Central Limit Theorem329(b) What is the probability that 20 cars chosen at random will have a meanload weight x of less than 74.5 tons of coal?(c) Interpretation Suppose the weight of coal in one car was less than74.5 tons. Would that fact make you suspect that the loader had slippedout of adjustment? Suppose the weight of coal in 20 cars selected at ran-dom had an average x of less than 74.5 tons. Would that fact make yoususpect that the loader had slipped out of adjustment? Why?Vital Statistics: Heights of Men The heights of 18-year-old men are ap-proximately normally distributed, with mean 68 inches and standard devia-tion 3 inches (based on information from Statistical Abstract of the UnitedStates, 112th edition).(a) What is the probability that an 18-year-old man selected at random isbetween 67 and 69 inches tall?(b) If a random sample of nine 18-year-old men is selected, what is theprobability that the mean height x is between 67 and 69 inches?(c) Interpretation Compare your answers to parts (a) and (b). Is the prob-ability in part (b) much higher? Why would you expect this?Medical: Blood Glucose Let x be a random variable that represents the levelof glucose in the blood (milligrams per deciliter of blood) after a 12-hour fast.Assume that for people under 50 years old, x has a distribution that is approx-imately normal, with mean u(based on information from Diagnostic Tests with Nursing Applications,edited by S. Loeb, Springhouse). A test result x < 40 is an indication ofsevere excess insulin, and medication is usually prescribed.(a) What is the probability that, on a single test, x < 40?(b) Suppose a doctor uses the average x for two tests taken about a weekapart. What can we say about the probability distribution of x? Hint: SeeTheorem 6.1. What is the probability that x < 40?(c) Repeat part (b) for n(d) Repeat part (b) for n(e) Interpretation Compare your answers to parts (a), (b), (c), and (d). Didthe probabilities decrease as n increased? Explain what this might implyif you were a doctor or a nurse. If a patient had a test result of x < 40based on five tests, explain why either you are looking at an extremelyrare event or (more likely) the person has a case of excess insulin.85 and estimated standard deviation o =25= 3 tests taken a week apart.5 tests taken a week apart.Medical: White Blood Cells Let x be a random variable that representswhite blood cell count per cubic milliliter of whole blood. Assume that xhas a distribution that is approximately normal, with mean u7500 andestimated standard deviation o =1750 (see reference in Problem 15). A testresult of x < 3500 is an indication of leukopenia. This indicates bone mar-row depression that may be the result of a viral infection.(a) What is the probability that, on a single test, x is less than 3500?(b) Suppose a doctor uses the average x for two tests taken about a weekapart. What can we say about the probability distribution of x? What isthe probability of I < 3500?(c) Repeat part (b) for n = 3 tests taken a week apart.(d) Interpretation Compare your answers to parts (a), (b), and (c). How did AND SAMPLING DISTRIBUTIONS6.Basic Computation: Central Limit Theorem Suppose x has a distributionwith a mean of 20 and a standard deviation of 3. Random samples of size36 are drawn.n =(a) Describe the x distribution and compute the mean and standard deviationof the distribution.(b) Find the z value corresponding to x =(c) Find P(I < 19).(d) Interpretation Would it be unusual for a random sample of size 36 fromthe x distribution to have a sample mean less than 19? Explain.19.7.| Statistical Literacy(a) If we have a distribution of x values that is more or less mound-shapedand somewhat symmetric, what is the sample size needed to claim thatthe distribution of sample means x from random samples of that size isapproximately normal?(b) If the original distribution of x values is known to be normal, do we need tomake any restriction about sample size in order to claim that the distributionof sample means x taken from random samples of a given size is normal?8.| Critical Thinking Suppose x has a distribution with(a) If random samples of size n = 16 are selected, can we say anything aboutthe x distribution of sample means?(b) If the original x distribution is normal, can we say anything about the xdistribution of random samples of size 16? Find P(68  6) smaller? Explain.(c) For which distribution is P(4 < x < 6) greater? Explain.81.13.| Coal: Automatic Loader Coal is carried from a mine in West Virginia to apower plant in New York in hopper cars on a long train. The automatic hoppercar loader is set to put 75 tons of coal into each car. The actual weights ofcoal loaded into each car are normally distributed, with mean u0.8 ton.75 tonsand standard deviation o =(a) What is the probability that one car chosen at random will have less than74.5 tons of coal?gage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-208

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