Problem 48E

In Exercise, use the following information. On a dry surface, the braking distances (in feet), from 60 miles per hour to a complete stop, of a sedan can be approximated by a normal distribution, as shown in the figure at the left.

What braking distance of a sedan represents the third quartile?

Solution :

Step 1 of 1:

The braking distances (in feet), from 60 miles per hour to a complete stop, of a sedan can be approximated by a normal distribution, the graph is

Our goal is:

We need to find braking distance of a sedan represents the third quartile.

From the given information the third quartile has a probability or area of 75% or 0.75 to its left.

Now we have to determine the z-score corresponding to the probability of 0.75.

Using area under the normal curve table,

z = 0.68

Then the value corresponding to the z-score is the mean increased by the product of the z-score and the standard deviation.

z =

0.68 =

129.5908

Therefore, braking distance of a sedan represents the third quartile is 129.5908.