What percent of Rafael Nadal’s first serves are between 100 and 110 mph? Please show work.

Question

In the 2008 Wimbledon tennis tournament, Rafael Nadal

averaged 115 miles per hour (mph) on his first serves. Assume

that the distribution of his first serve speeds is Normal with a

mean of 115 mph and a standard deviation of 6 mph.

The formula required to solve the problem is z= x-mean/standard deviation.

Answer 1

z(110) = -0.83333

z(100) = -2.5

 

Using my paper copy of standard normal distribution table...

P(Z<-2.5) = 0.00621

P(Z<-0.8333) = 0.20213 ... BY USE OF LINEAR INTERPOLATION

 

The difference in these probabilities is 0.19592, so I determine that 19.6% of Rafa's serves are between 100 & 110 mph.