Question: A transit system divides the region it serves into five fare zones. A survey of patrons was undertaken to study system use. The following table summarizes the results.

Zone Fare Percentage

1 Free 17.5

2 1.50 18.5

3 2.00 21.5

4 2.50 24.7

5 3.00 17.8

Find the following:

a) The mean fare of this system (7 points)

b) The variance of the appropriate probability distribution (10 points)

c) The standard deviation of the appropriate probability distribution (3 points).