The commuter train running between Orange County and downtown L.A. has an average speed of 60 mph with a standard deviation of 4.4 mph. As a consultant to the Dept. of Transportation in California, you examined 40 trains and recorded their average speeds.
1) What are the theoretical parameters for the sampling distribution based on these 40 trains? Assume you are dealing with an infinite population of trains.
2) What is the probability that the average speed of this sample of 40 trains will be less than 65 mph?
By central limit theorem, since the sample size 40 is large, the sample mean (i.e., the average speed of 40 trains), denoted as X, is approximately distributed as normal, ...
This solution is comprised of a detailed explanation of sampling exercises and the application of the normal distribution.