Empirical Rule

1. A group of Brigham Young University—Idaho students (Matthew Herring, Nathan Spencer, Mark Walker, and Mark Steiner) collected data on the speed of vehicles traveling through a construction zone on a state highway, where the posted (construction) speed limit was 25 mph. The recorded speeds for 14 randomly selected vehicles are given below: 

20, 24, 27, 28, 29, 30, 32, 33, 34, 36, 38, 39, 40, 40 

For this problem, you may round the mean to 32 and the sample standard deviation to 6. You may assume that it is appropriate to use the Empirical Rule. 

a. Use the Empirical Rule to estimate the percentage of speeds that are between 26 and 38 mph. 95%

b. Determine the actual percentage of drivers whose speeds were between 26 and 38 mph. That is, of the cars tracked, what percentage were actually going between 26 and 38 mph?

c. Use the Empirical Rule to determine the percentage of drivers who were speeding (whose speeds are 26 mph or higher). 

d. Find the z-score for a car driving 20 mph in this construction zone.

e. Find the z-score for a car driving 40 mph in this construction zone.
Is 95% correct for a?