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# Construct Frequency Distributions Classes

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1. Radiation in Baby Teeth: Listed below are amount of strontium-90 (in millibec-querels) in a simple random sample of baby teeth obtained from Pennsylvania residents born after 1979 (based on data from "An Unexpected Rise in Strontium-90 in U.S Deciduous Teeth in the 1990's ," by Mangano, et.al., Science of the Total Environment). Construct a frequency distribution with eight classes. Begin with a lower class limit of 110, and use a class width of 10. Cite a reason why such data are important.

155 142 149 130 151 163 151 142 156 133 138 161 128 144 172 137 151 166 147 163
145 116 136 158 114 165 169 149 150 150 150 158 151 145 152 140 170 129 188 156

2. Customer Waiting Times: Waiting times (in minutes) of customers at the Jefferson Valley Bank (where all customers enter a single waiting line) and the Bank of Providence (where customers wait in individual lines at three different teller windows) are listed below. Determine whether there is a difference between the two data sets that is not apparent from a comparison of the measures of center. If so, what is it?

Jefferson Valley (single line): 6.5 6.6 6.7 6.8 7.1 7.3 7.4 7.7 7.7 7.7
Providence (individual lines): 4.2 5.4 5.8 6.2 6.7 7.7 7.7 8.5 9.3 10.0

3. Identifying Events as Independent or Dependent: For each given pair of events, classify the two events as independent or dependent. (If two events are technically dependent but can be treated as if they are independent according to the 5% guideline, consider them to be independent.)

4. Using Composite Water Samples: The Orange County Department of Public Health tests water for contamination due to the presence of E. coli bacteria. To reduce laboratory costs, water samples from six public swimming areas are combined for one test, and further testing is done only if the combined sample fails. Based on past results, there is a 2% chance of finding E. coli bacteria in a public swimming area. Find the probability that a combined sample from six public swimming areas will reveal the presence of E. coli bacteria.

#### Solution Preview

1. Radiation in Baby Teeth: Listed below are amount of strontium-90 (in millibec-querels) in a simple random sample of baby teeth obtained from Pennsylvania residents born after 1979 (based on data from "An Unexpected Rise in Strontium-90 in U.S Deciduous Teeth in the 1990's ," by Mangano, et.al., Science of the Total Environment). Construct a frequency distribution with eight classes. Begin with a lower class limit of 110, and use a class width of 10. Cite a reason why such data are important.

155 142 149 130 151 163 151 142 156 133 138 161 128 144 172 137 151 166 147 163
145 116 136 158 114 165 169 149 150 150 150 158 151 145 152 140 170 129 188 156
Class Frequency
(110, 120] 2
(120, 130] 3
(130, 140] 5
(140, 150] 11
(150, 160] 10
(160, 170] 7
(170, 180] 1
(180, 190] 1
Where (110, 120] means that if x represents a value in the data set and , then x IS counted in that interval. The reason that this is necessary is because values like 150 COULD go into the category between 140 and 150 or the category between 150 and 160. This notation makes it clear what to do with an ...

#### Solution Summary

The expert constructs a frequency distribution class.

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