you should show all of your work.

Overall, the Miles Per Gallon for customers of MallState is normally distributed around 34 MPG with a standard deviation of 2.5 MPG.

In looking to reward environmentally friendly drivers, the insurer decides to reward drivers whose cars rank in the top 10%ile of MPG. What is the top 10%ile and which guest(s) from problem G would benefit from this program?

As a further commitment to the environment, customers at or below the 5%ile of MPGs will receive a free hybrid vehicle.What MPG does one need to stay below to be rewarded this way?

How likely is that somebody will drive a vehicle that gets a MPG between 35 and 37?

How likely it is that somebody will drive a vehicle that gets a MPG lower than 33MPG?

How likely it is to have a vehicle with MPG between 32 and 35MPG?

If 16 customers are selected at random, what's the likelihood that their mean MPG will be within 2 gallons of the population mean?

If 25 customers are selected at random, what's the likelihood that their mean MPG will be more than 35 miles per gallon?