2. If Z is a standard normal random variable find the following probabilities

a. P(Z 1.77)

b. P(-2.88 Z 2.15)

3. Studies show that gasoline use for compact cars sold in the United States is normally distributed, with mean use of 25.5 miles per gallon (mpg) and a standard deviation of 4.5 mpg.

a. What percentage of compact cars obtain 30 or more mpg?

b. In times of scarce energy resources a competitive advantage is given to automobile manufacturers who can produce a car obtaining substantially better fuel economy than the competitor's cars. If a manufacturer wishes to develop a compact car that outperform 95% of the current compacts in fuel economy, what must be the gasoline mileage for the new car?