Coursepack, p. 508 Math 133: 3.4 Worksheet #2 Name: Section #: 3.4: Measures of Position 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) c) Whose city has more pollution in absolute terms? (Circle One) Detroit Salt Lake City d) Whose city has more pollution in relative terms? (Circle One) Detroit Salt Lake City e) San Antonio, Texas, (in the west) had a z-score of 0. Explain what that means for San Antonio and its pollution index score. f) Boston, Massachusetts, (in the east) had a z-score of -0.767. Calculate Boston's pollution index score. (Give 1 decimal place and units. Show work)