A Stanford researcher recorded the speeds of cars passing a given checkpoint where the speed limit reads 20 mph. The mean of 100 randomly selected vehicles was 27, with a standard deviation of 3.5. (The measurements were taken over a two-month period) If the data truly represents all motorists traveling through this checkpoint and the data follows a normal distribution.

1. Sketch a normal distribution and label the intervals that represent one, two, and three standard deviations?

2. What proportion of motorists are expected to be traveling at the speed limit or slower? Greater than the speed limit?

3. What proportion of motorists are expected to be traveling at a speed between 20 and 30.5 mph?

4. What proportion of motorists are expected to be traveling at a speed between 27 and 34 mph?

5. What proportion of motorists are expected to be traveling at a speed greater than 37.5?

6. What percentage of motorists are expected to be traveling at a speed less than 25 mph?

7. What percentage of motorists are expected to be traveling at a speed greater than 29 mph?

8. What percentage of motorists are expected to be traveling at a speed between 25 and 33 mph?

9. What speed represents the 80th percentile? 10. What is the speed of the upper 1% of motorists passing this checkpoint?