Question

A construction zone on a highway has a posted speed limit of 40 miles per hour. The speeds of vehicles passing through this construction zone are normally distributed with a mean of 45 miles per hour and a standard deviation of 5.6 miles per hour. Find the percentage of vehicles passing through this construction zone that are exceeding the posted speed limit. Round to four decimal places.

Answer 1

X: speed of vehicle passing through this construction zone

X follows normal distribution with mean of 45 miles per hour and a standard deviation of 5.6 miles per hour

Speed limit : 40 miles per hour.

Probability of a vehicle passing through this construction zone that are exceeding the posted speed limit : P(X>40)

P(X>40) = 1- P(X40)

P(X40)

Z-score for 40 = (40-mean)/Standard deviation = (40-45)/5.6 = -5/5.6 = - 0.89

From standard normal table, P(Z-0.89) = 0.1867

P(X40) = P(Z-0.89) = 0.1867

P(X>40) = 1- P(X40) = 1 - 0.1867 = 0.8133

Probability of a vehicle passing through this construction zone that are exceeding the posted speed limit : P(X>40) = 0.8133

Percentage of vehicles passing through this construction zone that are exceeding the posted speed limit = 0.8133 x 100 = 81.33%