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.

Find the 85th percentile of Djokovic’s first-serve speeds.

117.2 mph
121.1 mph
116.1 mph
116.25 mph
106.8 mph

Answer 1

The 85th percentile of Djokovic's first-serve speeds is approximately 117.2 mph. Therefore correct option is A

Step-by-step explanation:

To find the 85th percentile of Djokovic's first-serve speeds, we need to calculate the z-score for this percentile and then convert it back to miles per hour.

First, we find the z-score using the formula:

z = (x - µ) / σ

where x is the value, µ is the mean, and σ is the standard deviation.

The 85th percentile corresponds to a z-score of approximately 1.036 and using this value, we can convert it back to miles per hour using the formula:

x = z * σ + µ

Plugging in the values, we get:

x = 1.036 * 5 + 112 = 117.18

So, the 85th percentile of Djokovic's first-serve speeds is approximately 117.2 mph.