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.)

The average height of adult American men is normally distributed with mean 70 inches and standard deviation 4 inches.

1. What's the probability that a randomly selected adult American man will be less than 75 inches tall?

2. NBA player Kobe Bryant is 6'6" tall. What proportion of adult American men are at least as tall as Kobe?

3. Find the 95^th percentile of adult American male heights.

The Toyota Prius has a mean fuel economy rating of 49.34 mpg with a population standard deviation of 0.46 mpg.

1. What is the probability that a randomly selected Prius gets more than 49.5 mpg?

2. A random sample of 15 Priuses is taken and the miles per gallon for each car are recorded. What is the probability that the mean mpg for this sample is more than 49.5 mpg?

3. A mechanic who services Priuses notices that the mean fuel economy of the 23 Priuses he services is 49.1 mpg. Should he be worried? (In other words, is this sample unusual? What is the probability of randomly getting a sample like this or worse?)

A union wants to get an idea of how many hours per month the average employee is absent from work. 325 employees are randomly selected, and the number of hours each employee misses work is recorded. If the sample has a mean of 8.1 hours and a standard deviation of 5.8 hours,

1. Give a 95% confidence interval for the mean number of hours per month an employee is absent.

2. Give a 99% confidence interval for the mean number of hours per month an employee is absent. How does this interval differ from the one above? Why does this happen?

3. Suppose we know that the population standard deviation for the number of missed hours per month is actually 5.4. Give a 95% confidence interval for the mean number of hours per month an employee is absent, given this new piece of information.