Reliable Trucking Company determined that, on annual basis, the distance traveled for each truck is normally distributed with average of 58,000 miles and tandard deviation of 7,500 miles.
a. What percentage of trucks can be expected to travel between 51,250 and 62,500 miles?
b. What proportion of trucks can be expected to travel either less than 55,000 miles or more than 66,250 miles?
c. Suppose the average miles expected to travel by these trucks is unknown, but there is a 14% chance that the truck will travel over 70,000 miles. Assuming the standard deviation is still 7,500 miles, what would be the mean travel distance of these trucks?
d. Suppose the standard deviation of the traveling distance of these trucks is unknown, but there is a 92% chance that the trucks will travel at least 44,500 miles. Assume the mean traveling distance is 58,000 miles. What would be the standard deviation of the travel distance of the Reliable Trucking Company's trucks?