Solve the following:
Introduced in the 2000 model year, the Honda Insight was the first hybrid automobile sold in the United States. The mean gas mileage for the model year 2005 Insight with an automatic transmission is 56 mpg on the highway. Assume the gasoline mileage of this mileage is approximately normally distributed with a standard deviation of 3.2 miles per gallon.
a. What proportion of 2005 Honda Insights with automatic transmission gets over 60 mpg on the highway?
b. What proportion of 2005 Honda Insights with automatic transmission gets 50 mpg or less on the highway?
c. What proportion of 2005 Honda Insights with automatic transmission gets between 58 and 62 miles per gallon on the highway?
d. What is the probability that a randomly selected Honda Insight with an automatic transmission gets less than 45 miles per gallon on the highway?
e. What is the probability that a randomly selected Honda Insight with an automatic transmission gets more than 56 miles per gallon on the highway?