For questions 4 through 9, please use the yearly robbery counts for a metropolitan area in the Midwest to answer the questions. These include the number of robberies, per year, from 2009 through 2018.20092010201120122013201420152016201720185904234264456035795435825396804. (5 points). Measures of Central Tendency. Please use the robbery data to calculate and report on the below.a. Mean:b. Median:c. Mode:5. (5 points). Measures of Variability. Please use the robbery data to calculate and report on the below (Hint: treat all distributions as populations).a. Range:b. Variance:c. Standard Deviation:6. (5 points). Z-scores. Please use the robbery data to calculate the Z-scores for the below values.a. 423:b. 603:c. 543:d. 582:e. 680:7. (10 points). Area under the curve. Identify what percentage of the distribution should be found under the curve using the below information. Although not graded, it may be helpful to draw the corresponding normal distribution where that percentage is located (either here if you know how or on a piece of scrap paper for your own reference). An example is provide below.Example: What percentage of the distribution would we expect to fall between the Z-score for the value of 426 from the original distribution and a Z-score of 0?The Z-score associated with 1,416 is -1.25. We would expect 39.44% of the distribution to fall between the Z-scores of -1.25 and 0.a. What percentage of the distribution would we expect to fall between the Z-score for the value of 423 from the original distribution and a Z-score of 0b. What percentage of the distribution would we expect to fall between the Z-score for the value of 603 from the original distribution and a Z-score of 0?c. What percentage of the distribution would we expect to fall between the Z-score for the value of 543 and the rest of the distribution to the right of that value?d. What percentage of the distribution would we expect to fall between the Z-score for the value of 582 and the rest of the distribution to the right of that value?e. What percentage of the distribution would we expect to fall between the Z-score for the value of 423 from the original distribution and the Z-score for the value of 680 from the original distribution?8. (5 points). Standard Error of the Mean. What is the standard error of the mean for the following values sampled from the population of Seattle robberies: 426, 445, 603, 579, 543. (Also treat these five numbers as a population when calculating their standard deviation)9. (5 points). Standard Error Z-scores & Area under the curvea. What is the Z-score associated with the standard error of the mean you calculated in question 8?b. What percentage of a normal distribution would we expect to fall between the Z-score for the standard error of the mean and a Z-score of 0?For more information on Standard Error of The Mean check on: https://simple.wikipedia.org/wiki/Standard_error
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