An important quality characteristic of water is the concentration of suspended solid material. Below are 60 measurements of suspended solids from a certain lake.

42.4, 65.7, 29.8, 58.7, 52.1, 55.8, 57.0, 68.7, 67.3, 67.3, 54.3, 54.0, 73.1, 81.3, 59.9, 56.9, 62.2, 69.9, 66.9, 59.0, 56.3, 43.3, 57.4, 45.3, 80.1, 49.7, 42.8, 42.4, 59.6, 65.8, 61.4, 64.0, 64.2, 72.6, 72.5, 46.1, 53.1, 56.1, 67.2, 70.7, 42.6, 77.4, 54.7, 57.1, 77.3, 39.3, 76.4, 59.3, 51.1, 73.8, 61.4, 73.1, 77.3, 48.5, 89.8, 50.7, 52.0, 59.6, 66.1, 31.6

Construct a normal probability plot. Does it seem reasonable to assume that the concentration of suspended solids is normally distributed?

We would analyze the given data by constructing a normal probability plot and then determining whether the data is normally distributed based on whether or not the points in the plot generally align along a straight line. It's also important to bear in mind that there may be other factors influencing the distribution.

Explanation:

To answer this question, we would first list the given measurements of suspended solids and sort these measurements in ascending order. Then, we would plot these sorted values against corresponding z-scores (values from a standard normal distribution corresponding to the cumulative proportions in our sample) - this will give us a normal probability plot. To determine whether it is reasonable to assume that the concentration of the suspended solids is normally distributed, we would look at the resulting plot.

If the points generally follow a straight line, then it is reasonable to assume that the data is normally distributed. This is based on the concept of the Normal or Gaussian probability distribution. It's also worth noting that while this can provide a good initial check, it may not perfectly capture the actual distribution and there could be influences from outliers or other factors. Even 'normal-looking' data can violate the assumption of normality upon further statistical tests.

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