Vehicle speeds at a certain highway location are believed to be approximately normally distributed with a mean of 60 mph and standard deviation of 6 mph. For each of the following questions, fill in the blank with the appropriate speeds. Apply the Empirical Rule.
a. One vehicle is randomly selected; there is about a 68% that the vehicle's speed will be between ___ and ___.
b. One vehicle is randomly selected; there is about a 95% chance that the vehicle's speed will be between ___ and ___.
c. The speeds of randomly selected samples of 16 vehicles will be recorded. For samples of vehicles, there is about a 68% chance that a sample's mean speed will be between ___ and ___.
d. The speeds of randomly selected samples of 36 vehicles will be recorded. For samples of vehicles, there is about a 95% chance that a sample's mean speed will be between ___ and ___.
e. The speeds of one randomly selected sample of 36 vehicles were recorded. The sample mean was 57 mph. What is the probability, given and , that a sample of would have a mean of 57 mph or less?
f. Given your results from part (e), do you think it is likely that this sample of 36 vehicles came from a population with ? Why or why not?