Draw a picture of the distribution for each problem with mean and standard deviations labeled and relevant areas shaded. Show exactly what you entered in to the calculator to arrive at your result, including what function you used and what numbers you entered. Round all decimals to 3 places. Read the questions carefully!

The average life of a new type of motor is normally distributed with mean 10 years and standard deviation 2 years.

1. What proportion of these motors will last somewhere between 8 and 11 years?

2. What's the probability that a randomly selected motor will last more than 15 years?

3. The manufacturer of these motors wants to offer a warranty. If the motor stops working before the warranty period is up, the manufacturer will replace it for free. If that manufacturer is willing to replace only 5% of the motors that they produce, how long should they make the warranty? (In other words, find the number of years n such that 95% of all motors have a life longer than n.)