The data below represent the average sulfur dioxide content over the years 1969-

Question

The data below represent the average sulfur dioxide content over the years 1969-1971 in 41 US cities (measured in micrograms per cubic meter). Determine if the data arise from a normal distribution. ["I understand how to make the histogram. I need help on calculating z-scores and after."]
Hint: Use Sturge’s rule to construct a histogram of the data. Using the mean and standard deviation calculated from the sample data, determine the z-scores for the class upper and lower limits. The z-score for the upper limit of one bin should be identical to the z-score of the lower limit of the adjoining bin. Then, determine the probability that a value will fall between the lower and upper limit of the bin, if it were a normal distribution. Use this probability to determine the expected value of each bin. Finally, compare this expected value to observed values (the actual frequency) seen in each bin. Show your calculations for the first bin only. You may use Excel or a calculator for the remaining bins.
Sulfur dioxide content in US cities:           10        13        12        17        56        36        29        14        10        24      110      28        17        8          30        9          47        35        29        14        56        14        11        46        11      23        65        26        69        61        94        10        18        9          10        28        31        26        29        31      16


Hint: Use Sturge’s rule to construct a histogram of the data. Using the mean and standard deviation calculated from the sample data, determine the z-scores for the class upper and lower limits. The z-score for the upper limit of one bin should be identical to the z-score of the lower limit of the adjoining bin. Then, determine the probability that a value will fall between the lower and upper limit of the bin, if it were a normal distribution. Use this probability to determine the expected value of each bin. Finally, compare this expected value to observed values (the actual frequency) seen in each bin. Show your calculations for the first bin only. You may use Excel or a calculator for the remaining bins.
Sulfur dioxide content in US cities:           10        13        12        17        56        36        29        14        10        24      110      28        17        8          30        9          47        35        29        14        56        14        11        46        11      23        65        26        69        61        94        10        18        9          10        28        31        26        29        31      16

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