Chapter 2: Problem 75
What is advantage of the range as a measure of variability?
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
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Chapter 2: Problem 75
What is advantage of the range as a measure of variability?
These are the key concepts you need to understand to accurately answer the question.
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What do you mean by a mound-shaped, symmetric distribution?
The U.S. Environmental Protection Agency (EPA) sets a limit on the amount of lead permitted in drinking water. The EPA Action Level for lead is .015 milligram per liter (mg/L) of water. Under EPA guidelines, if \(90 \%\) of a water system's study samples have a lead concentration less than \(.015 \mathrm{mg} / \mathrm{L},\) the water is considered safe for drinking. I (coauthor Sincich) received a report on a study of lead levels in the drinking water of homes in my subdivision. The 90th percentile of the study sample had a lead concentration of \(.00372 \mathrm{mg} / \mathrm{L}\). Are water customers in my subdivision at risk of drinking water with unhealthy lead levels? Explain.
Why do we square the deviation from the mean before adding them to compute the variance?
Graph the relative frequency histogram for the 500 measurements summarized in the accompanying relative frequency table.$$ \begin{array}{cc} \text { Class Interval } & \text { Relative Frequency } \\ \hline .5-2.5 & .10 \\ 2.5-4.5 & .15 \\ 4.5-6.5 & .25 \\ 6.5-8.5 & .20 \\ 8.5-10.5 & .05 \\ 10.5-12.5 & .10 \\ 12.5-14.5 & .10 \\ 14.5-16.5 & .05 \end{array} $$
Freckles are defects that sometimes form during the solidification of alloy ingots. A freckle index has been developed to measure the level of freckling on the ingot. A team of engineers conducted several experiments to measure the freckle index of a certain type of superalloy (Journal of Metallurgy, Sept. 2004 ). The data for \(n=18\) alloy tests are shown in the table. $$ \begin{array}{rrrrrr} \hline 12.6 & 22.0 & 4.1 & 16.4 & 1.4 & 2.4 \\ 16.8 & 10,0 & 3.2 & 30.1 & 6.8 & 14.6 \\ 2.5 & 12.0 & 33.4 & 22.2 & 8.1 & 15.1 \\ \hline \end{array} $$ a. Construct a box plot for the data and use it to find any outliers. b. Find and interpret the z-scores associated with the alloys you identified in part a.
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