After increased patrol,91% of vehicles on a road travel above 45 km/h with a standard deviation of 5.2 km/h.Assuming a Normal model is appropriate,find the mean speed.
A)40.95 km/h
B)50.2 km/h
C)-38.03 km/h
D)4.73 km/h
E)51.97 km/h

Question

Quizplus · Accepted Answer

The mean speed is the value we're trying to find, and the problem states that 91% of the vehicles travel above 45 km/h. In a normal distribution, 91% above a certain value means that value is 1.34 standard deviations below the mean (using a Z-table or standard normal distribution table). Thus, we calculate the mean as follows: Mean = 45 km/h + (1.34 * 5.2 km/h) = 45 km/h + 6.97 km/h = 51.97 km/h.

After Increased Patrol,91% of Vehicles on a Road Travel Above