In 2017 a pollution index was calculated for a sample of cities in the eastern states using data on air and water pollution. Assume the distribution of pollution indices is unimodal and symmetric. The mean of the distribution was 35.9 points with a standard deviation of 11.6 points.

a. What percentage of eastern cities would you expect to have a pollution index between 12.7 and 59.1 points?

b. What percentage of eastern cities would you expect to have a pollution index between 24.3 and 47.5 points? 

c. The pollution index for New York, in 2017 was 58.7 points. Based on this distribution, was this unusually high? Explain.