Given:

On a particular highway, a permanent speed measuring device at one particular location has determined, over many months of observations, that the mean and standard deviation of vehicle speeds at that point are 52 miles per hour and 4 miles per hour, respectively. An engineer wonders if the same speed distribution holds at a spot a mile down the road. The sample mean of 20 vehicle speeds collected at that location is 50 miles per hour, somewhat less than the mean at the reference location. The sample standard deviation of the speeds at the second location was 6 miles/hour.

Find:

a. What distribution can be reasonably assumed for the sample mean?

b. If the same speed distribution holds in both locations, what is the probability of observing a speed at least this far below the reference mean?

c. What distribution can be reasonably assumed for the sample variance?

d. If the .same distribution holds in both locations, what is the probability of observing a sample standard deviation at least as large as what was seen at the second location?