#17 (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?14.| 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?15.| 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 µ(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 =253 tests taken a week apart.5 tests taken a week apart.16.| 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 u =7500 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 i for two tests taken about a weekapart. What can we say about the probability distribution of x? What isthe probability of x < 3500?(c) Repeat part (b) for n(d) Interpretation Compare your answers to parts (a), (b), and (c). How didthe probabilities change as n increased? If a person had x < 3500 basedon three tests, what conclusion would you draw as a doctor or a nurse?3 tests taken a week apart.17.| Wildlife: Deer Let x be a random variable that represents the weights inkilograms (kg) of healthy adult female deer (does) in December in MesaVerde National Park. Then x has a distribution that is approximately normal,with mean u63.0 kg and standard deviation o7.1 kg (Source: TheMule Deer of Mesa Verde National Park, by G. W. Mierau and J. L. Schmidt,jhts Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-208 PLING DISTRIBUTIONSMesa Verde Museum Association). Suppose a doe that weighs less than 54 kgis considered undernourished.(a) What is the probability that a single doe captured (weighed and released)at random in December is undernourished?(b) If the park has about 2200 does, what number do you expect to be under-nourished in December?(c) Interpretation To estimate the health of the December doe population,park rangers use the rule that the average weight of nbe more than 60 kg. If the average weight is less than 60 kg, it is thoughtthat the entire population of does might be undernourished. What is theprobability that the average weight i for a random sample of 50 does isless than 60 kg (assume a healthy population)?(d) Interpretation Compute the probability that i < 64.2 kg for 50does (assume a healthy population). Suppose park rangers captured,weighed, and released 50 does in December, and the average weight wasx = 64.2 kg. Do you think the doe population is undernourished or not?Explain.50 does shouldFocus Problem: Impulse Buying Let x represent the dollar amount spent onsupermarket impulse buying in a 10-minute (unplanned) shopping interval.Based on a Denver Post article, the mean of the x distribution is about $20and the estimated standard deviation is about $7.(a) Consider a random sample of n10 minutes of unplanned shopping time in a supermarket. From the centrallimit theorem, what can you say about the probability distribution of x,the average amount spent by these customers due to impulse buying?What are the mean and standard deviation of the x distribution? Is itnecessary to make any assumption about the x distribution? Explain.(b) What is the probability that x is between $18 and $22?(c) Let us assume that x has a distribution that is approximately normal.What is the probability that x is between $18 and $22?(d) Interpretation: In part (b), we used x, the average amount spent, com-puted for 100 customers. In part (c), we used x, the amount spent by onlyone customer. The answers to parts (b) and (c) are very different. Whywould this happen? In this example, x is a much more predictable or reli-able statistic than x. Consider that almost all marketing strategies andsales pitches are designed for the average customer and not the individualcustomer. How does the central limit theorem tell us that the average cus-100 customers, each of whom hastomer is much more predictable than the individual customer?Finance: Templeton Funds Templeton World is a mutual fund that investsin both U.S. and foreign markets. Let x be a random variable that representsthe monthly percentage return for the Templeton World fund. Based oninformation from the Morningstar Guide to Mutual Funds (available in mostlibraries), x has mean µ1.6% and standard deviation o =0.9%.(a) Templeton World fund has over 250 stocks that combine together to givethe overall monthly percentage return x. We can consider the monthlyreturn of the stocks in the fund to be a sample from the population ofmonthly returns of all world stocks. Then we see that the overall monthly

Name: #17 (c) Interpretation Suppose the weight of coal in one car was less
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Description: #17 (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 tha

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Mesa Verde Museum Association). Suppose a doe that weighs less than 54 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (b) If the park has about 2200 does, what number do you expect to be under- nourished in December? (c) Interpretation To estimate the health of the December doe population, park rangers use the rule that the average weight of n = be more than 60 kg. If the average weight is less than 60 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample less than 60 kg (assume a healthy population)? (d) Interpretation Compute the probability that i< 64.2 kg for 50 does (assume a healthy population). Suppose park rangers captured, weighed, and released 50 does in December, and the average weight was 64.2 kg. Do you think the doe population is undernourished or not? Explain. 50 does should 50 does is