A construction zone on a highway has a posted speed limit of 35 miles per hour. Data collection shows that the speeds of vehicles passing through this construction zone are normally distributed with a mean of 37 miles per hour and a standard deviation of 5 miles per hour. In your analysis below,

• Draw a sketch of the normal distribution to estimate probabilities and values.
• Use the appropriate technological tool to make your calculations.
• Be sure to interpret the results of your calculations.

What percentage of drivers are driving between 40 and 50 miles per hour?

What percentage of drivers are speeding through the construction zone?

The state police would like to prevent drivers from speeding dangerously through construction zones. They will fine the most hazardous 20% of drivers with a $500 ticket. What is the minimum speed that would put a driver into this top 20%?