Question

professional tennis player novak djokovic hits the ball extremely hard. his first-serve speeds can be modeled by a normal distribution with mean 112 miles per hour (mph) and standard deviation 5 mph.
how often does djokovic hit his first serve faster than 120 mph?
94.52%
1.60%
5.48%
10.96%

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x = 120\), \(\mu=112\), and \(\sigma = 5\).

$$z=\frac{120 - 112}{5}=\frac{8}{5}=1.6$$

Step2: Find the probability using the standard normal distribution table

We want to find \(P(X>120)\), which is equivalent to \(P(Z > 1.6)\).
Since \(P(Z>z)=1 - P(Z\leq z)\), and from the standard normal distribution table \(P(Z\leq1.6)=0.9452\).

$$P(Z > 1.6)=1-0.9452 = 0.0548$$

Answer:

\(5.48\%\)