Answer to Question #293511 in Statistics and Probability for safa

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 87 miles per hour (mph) and the standard deviation of the serve speeds was 13 mph. Assume that the statistician also gave us the information that the distribution of the serve speeds was bell shaped. Use the 68-95-99.7 rule to answer the following questions.

a) What is the approximate percentage of serves between 48 and 126? Do not enter the percent symbol.

Answer 1

68–95–99.7 rule

$$P(\mu-1\sigma\leq X\leq\mu+1\sigma)\approx0.6827$$

$$P(\mu-2\sigma\leq X\leq\mu+2\sigma)\approx0.9545$$

$$P(\mu-3\sigma\leq X\leq\mu+3\sigma)\approx0.9973$$

$$\mu-3\sigma=87-3(13)=48$$

$$\mu+3\sigma=87+3(13)=126$$

$$P(48<X<126)=P(\mu-3\sigma\leq X\leq\mu+3\sigma)$$

$$\approx0.9973$$

$99.73$