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. what percentage of djokovics first serves are slower than 100 mph? 2.40% 1.64% 0.82% 99.18%

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 100$, $\mu=112$, and $\sigma = 5$.
$z=\frac{100 - 112}{5}=\frac{-12}{5}=- 2.4$

Step2: Find the probability using the standard normal distribution table

We want to find $P(X\lt100)$, which is equivalent to $P(Z\lt - 2.4)$ using the standard normal distribution (since $Z=\frac{X-\mu}{\sigma}$).
Looking up the value of $z=-2.4$ in the standard normal distribution table (the area to the left of $z$ - value). The value corresponding to $z =-2.4$ is $0.0082$.

Answer:

C. $0.82\%$