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 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?)