The speeds in miles per hour of motor vehicles on a certain

The speeds (in miles per hour) of motor vehicles on a certain stretch of Route 3A as clocked at a certain place along the highway are normally distributed with a mean of 67.8 mph and a standard deviation of 7.82 mph. What is the probability that a motor vehicle selected at random is traveling at the following speeds? (Round your answers to four decimal places.)

(a) more than 71 mph

(b) less than 63 mph

(c) between 71 and 76 mph

Solution

Given that mean=67.8 and standard deviation sd=7.82
We need to find z-score using given formula
z = (x-mean)/sd

Ans a).
z=(71-67.8)/7.82=0.409207161125
which corresponds to a probability of 0.658806.
This is the probability that the speed is less than 71, so the probability that the speed is more than 71 is 1-0.658806 = 0.341194

Ans b).
z=(63-67.8)/7.82=-0.613810741688
which corresponds to a probability of 0.26967

Ans c).
z=(76-67.8)/7.82=1.04859335038 which corresponds to a probability of 0.852817
z=(71-67.8)/7.82=0.409207161125 which corresponds to a probability of 0.658806.
So required probability will be difference of both which is = 0.852817-0.658806= 0.194011