1. In 2017, a pollution index was calculated for a sample of cities in the western and eastern states in the U.S using data on air and water pollution. The eastern cities had a mean of 35.9 points with a standard deviation of 11.6 points. The western cities had a mean of 43.0 points, with a standard deviation of 11.3 points. Higher scores means more pollution (which is not good). Assume the distributions of pollution indices approximately bell-shaped. (Source) a) Detroit, Michigan, (in the east) had a pollution index score of 56.2. Calculate its z-score. (Give 2 decimal places and show work) b) Salt Lake City, Utah, (in the west) had a pollution index score of 61.4. Calculate its z-score. (Give 2 decimal places and show work)