1. Over a very long period of time, a sheriff determines the meanvehicle speed on a road is 67 miles per hour, the standarddeviation is 3 miles per hour. Treat this as the population, not asample.
   1. If the speed limit is 60 miles per hour, what percentage of thevehicles exceed the speed limit?
   2. The sheriff cracks down on speeders. His deputies ignore anyvehicles going less than 63 mph, and issue warnings to those goingbetween 63 and 65, and issue tickets to those going faster than 65mph.
      1. What percentage will get warnings?
      2. What percentage will get tickets?

Following the crackdown, the sherifftakes a random sample (n=84) of vehicle speeds on the road way. Hissample data: mean is 63 mph, sample SD is 4 mph.

1. Calculate the standard error of the sample mean using thesample standard deviation, and applying the +/- 2 rule of thumb,calculate the 95% confidence interval around the sample mean
2. A county commissioner claims that the crackdown had no effect,and the average speed is still 67 mph. Is this commissionercorrect?
   1. How likely is it that the sample of came from a populationwhere the average speed is 67?
3. What if the sheriff’s post-crackdown random sample was not n=84but in fact n=30? Assume the sample mean and standard deviationwere unchanged. Use a t-table to determine the 95% confidenceinterval around that sample mean.
   1. Would the county commissioner be accurate in this case?