Question

At a tennis tournament a statistician keeps track of every serve. The statistician reported that the mean serve speed of a particular player was 96 miles per hour and the standard deviation of the serve speed was 12 mph. Assume the statistician also gave us the information that the distribution of the serve speeds was bell-shaped. What proportion of the player's serves are expected to be between 108 mph and 132 mph?

Answer 1

First, convert the 112 and 130 to z-scores:

z1 = (112 - 103) / 9 = 1

z2 = (130 - 103) / 9 = 3

Now find the area under the normal curve between z = 1 and z = 3. You can do this by looking in a z-table. I will do it using my TI-83:

normalcdf(1,3) = .1573052923 <----answer