In the article “Occurrence and Distribution of Ammonium in Iowa Groundwater”, ammonium concentrations (in mg/L) were measured at a large number of wells in the state of Iowa. The mean concentration was 0.71, the median was 0.22, and the standard deviation was 1.09. Is it possible to determine whether these concentrations are approximately normally distributed? If so, say whether they are normally distributed, and explain how you know. If not, describe the additional information you would need to determine whether they are normally distributed.
What will be an ideal response?
The concentrations are not approximately normally distributed. There are no concentrations lower than 0, and 0 is only 0.71/1.09 = 0.65 standard deviations below the mean. In a normal distribution, approximately 26% of the values would be farther below the mean than this. In addition, the mean is much larger than the median, which is uncharacteristic of a sample from a normal distribution.
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