In 2017, a pollution index was calculated for a sample of cities in the eastern states using data on air and water pollution. It is assumed that the distribution of pollution indices is unimodal and symmetric. The mean of the distribution was 37.6 points with a standard deviation of 11.4 points.
Complete parts (a) through (c) below.
a. What percentage of eastern cities would you expect to have a pollution index between 14.8 and 60.4 points?
b. What percentage of eastern cities would you expect to have a pollution index between 26.2 and 49.0 points?
c. The pollution index for an eastern city in 2017 was 44.2 points. Based on this distribution, was this unusually high? Explain.
A. Yes, because 44.2 falls within three standard deviations of the mean, so it is therefore an unusually high pollution index.
B. No, because 44.2 falls exactly two standard deviations away from the mean, and it is therefore not an unusually high pollution index.
C. No, because 44.2 falls within two standard deviations away from the mean, and it is therefore not an unusually high pollution index.
D. Yes, because 44.2 falls within two standard deviations of the mean, so it is therefore an unusually high pollution index.