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Chapter 6: Normal Probability Distributions

Q3

Page 281

Small Sample Data set 29 鈥淐oin Weights鈥 in Appendix B includes weights of 20 one-dollar coins. Given that the sample size is less than 30, what requirement must be met in order to treat the sample mean as a value from a normally distributed population? Identify three tools for verifying that requirement.

Q3

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Standard Normal Distribution Identify the two requirements necessary for a normal distribution to be a standard normal distribution

Q3

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Notation In general, what do the symbols x and x represent? What are the values of xand xfor samples of size 64 randomly selected from the population of IQ scores with population mean of 100 and standard deviation of 15?

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What is the difference between a standard normal distribution and a non-standard normal distribution?

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Bone Density Test. In Exercises 1鈥4, assume that scores on a bone mineral density test are normally distributed with a mean of 0 and a standard deviation of 1.

Bone Density For a randomly selected subject, find the probability of a score greater than -2.93.

Q3

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Unbiased Estimators Data Set 4 鈥淏irths鈥 in Appendix B includes birth weights of 400 babies. If we compute the values of sample statistics from that sample, which of the following statistics are unbiased estimators of the corresponding population parameters: sample mean; sample median; sample range; sample variance; sample standard deviation; sample proportion?

Q3

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In Exercises 1-3, use the following recent annual salaries (in millions of dollars) for players鈥俹n鈥倀he鈥侼.Y.鈥侹nicks鈥俻rofessional鈥俠asketball鈥倀eam.

23.4, 22.5, 11.5 ,7.1 ,6.0 ,4.1 ,3.3, 2.8, 2.6, 1.7, 1.6 ,1.3, 0.9 ,0.9, 0.6.

NY Knicks Salaries Round each of the salaries to the nearest million dollars, then construct a dot plot. Do the values appear to be from a population having a normal distribution?

Q30

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Standard Normal DistributionIn Exercises 17鈥36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given bone density test scores. If using technology instead of Table A-2, round answers

to four decimal places.

Between -3.00 and 3.00.

Q30

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Body Temperatures Based on the sample results in Data Set 3 鈥淏ody Temperatures鈥 in Appendix B, assume that human body temperatures are normally distributed with a mean of 98.20掳F and a standard deviation of 0.62掳F.

a. According to emedicinehealth.com, a body temperature of 100.4掳F or above is considered to be a fever. What percentage of normal and healthy persons would be considered to have a fever? Does this percentage suggest that a cutoff of 100.4掳F is appropriate?

b. Physicians want to select a minimum temperature for requiring further medical tests. What should that temperature be, if we want only 2.0% of healthy people to exceed it? (Such a result is a false positive, meaning that the test result is positive, but the subject is not really sick.)

Q31

Page 241

Standard normal distribution, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, Draw a graph, then find the probability of the given bone density test score. If using technology instead of Table A-2, round answers to four decimal places.

Between -1.00 and 5.00

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