Question

Info: 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 37.6 points with a standard deviation of 11.1 points. Answer question 10 to question 12 below.

part A: What percentage of eastern cities would you expect to have a pollution index between 15.4 and 59.8 points?

Select one:

a. 99.7%

b. 95%

c. 68%

part B: What percentage of eastern cities would you expect to have a pollution index between

26.5 and 48.7 ​points?

Select one:

a. 99.7%

b. 95%

c. 68%

part C: The pollution index for an eastern city, in 2017, was 43.9 points. Based on this distribution, was this unusually high? Explain.

Select one:

a. ​Yes, because 43.9 falls within three standard deviations of the​ mean, so it is therefore an unusually high pollution index.

b. No, because 43.9 falls exactly two standard deviations away from the​ mean, and it is therefore not an unusually high pollution index.

c. Yes, because 43.9 falls within two standard deviations of the​ mean, so it is therefore an unusually high pollution index.

d. ​No, because 43.9 falls within two standard deviations away from the​ mean, and it is therefore not an unusually high pollution index.

Answer 1

Part A :

b. 95%

Part B :

c. 68%

Part C :

d. No , because 43.9 falls within two standard deviations away from the​ mean, and it is therefore not an unusually high pollution index