The file Tax contains the quarterly sales tax receipts (in $thousands) submitted to the comptroller of the Village of Fair Lake for the period ending March 2011 by all 50 business establishments in that locale:
10.3 11.1 9.6 9.0 14.5 13.0 6.7 11.0 8.4 10.3
8.0 11.2 7.3 5.3 12.5 8.0 11.8 8.7 10.6 9.5
11.1 10.2 11.1 9.9 9.8 11.6 15.1 12.5 6.5 7.5
10.0 12.9 9.2 10.0 12.8 12.5 9.3 10.4 12.7 10.5
9.3 11.5 10.7 11.6 7.8 10.5 7.6 10.1 8.9 8.6
a. Compute the mean, variance, and standard deviation for this population.
b. What percentage of the 50 businesses has quarterly sales tax receipts within ± 1, 2, or ±3 standard deviations of the mean?
c. Compare your findings with what would be expected on the basis of the empirical rule. Are you surprised at the results in (b)?