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Isabelle was curious if sample maximum was an unbiased estimator of population maximum. She started with a large normally distributed population of test scores whose
Isabelle was curious if sample maximum was an unbiased estimator of population maximum. She started with a large normally distributed population of test scores whose maximum was \[99\] points. She then took a random sample of \[6\] tests and calculated the maximum of the sample. She replaced those tests and repeated this process for a total of \[40\] trials. Her results are summarized in the dotplot below, where each dot represents the maximum score from a sample of \[6\] tests. A dot plot for a sample maximum has a scale from 75 to 100. The number of dots for each is as follows. 78, 1. 79, 1. 80, 3. 81, 2. 82, 5. 83, 2. 84, 2. 85, 2. 86, 3. 87, 3. 88, 1. 89, 4. 90, 2. 91, 1. 92, 2. 93, 3. 94, 3. 94, 3. 95, 0. 96, 0. 97. 1. \[75\] \[80\] \[85\] \[90\] \[95\] \[100\] Based on these results, does sample maximum appear to be a biased or unbiased estimator of population maximum? Hint: The population maximum is \[99\]
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