Marathon run times follow a normal distribution with mean equal to five hours and standard deviation equal to 2 *19.

1. What are the marathon run times for the middle 68% of runners? (hint from ... to ... minutes)

2. What are the marathon times for the middle 95% of the runners? (hint from ... to ... minutes)

3. How fast did the top 16% of the fastest runners run the marathon? (hint: faster than ..)

4. How slow are the slowest 2.5% of runners? (hint slower than...)

5. What percentage of runners run faster than 295 minutes? (hint: use the standard score)

6. How fast are the fastest 5% of runners?

7. How slow are the slowest 1% of runners?

(hint 1) for the first 4 problems you can use the 68-95-99.7 rule or the diagrams we discussed in class. For the rest of the problems problems you need to use the standard normal table or z-score table also discussed in class. (hint 2) Draw the distribution and shade the area you want to calculate).