Find the percentage of vehicles passing through this construction zone that are traveling at a speed of 50 and 57 miles per hour.

Question

a construction zone on a highway has a posted speed limit of 40 per hour. The speedspeed of vehicles passing through this construction zone are normally distributed with a mean of 46 miles per hour and a standard deviation of 4 miles per hour. Find the percentage of vehicles passing through this construction zone that are traveling at a speed of 50 and 57 miles per hour.

Answer 1

Z for 57 mph = (57-46)/4 = 11/4 = 2.75.  Looking that up on a Z-score table gives a percentile = 0.9970.

 

Z for 50 mph = (50-46)/4 = 4/4 = 1. Looking that up on the Z score table gives a percentile = 0.8413.

 

Percentage of vehicles between 50 and 57 mph = 0.9970 - 0.8413 = 0.1557 = 15.57%