## Related questions with answers

In 2017 a pollution index was calculated for a sample of cities in the western states using data on air and water pollution. Assume the distribution of pollution indices is unimodal and symmetric. The mean of the distribution was 43.0 points with a standard deviation of 11.3 points.

a. What percentage of western cities would you expect to have a pollution index between 31.7 and 54.3 points?

b. What percentage of western cities would you expect to have a pollution index between 20.4 and 65.6?

c. The pollution index for San Jose in 2017 was 51.9 points. Based on this distribution, was this unusually high? Explain.

Solution

Verifieda. Approximately $68\%$ of western cities which is within one standard deviation of the mean, respectively,

$\begin{aligned} (31.7\ \text{to}\ 54.3) = (43.0 - 11.3\ \text{to}\ 43.0 + 11.3), \end{aligned}$

as shown in Graph 1,

Graph 1. The display of the $68\%$ of the data

The green area is about $68\%$ of the area under the curve.

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