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.

Answer 1

To find the 85th percentile of Djokovic's first-serve speeds, use the standard normal distribution table to find the corresponding z-score and then convert it back to the original units.

Step-by-step explanation:

To find the 85th percentile of Djokovic's first-serve speeds, we can use the standard normal distribution table. First, convert the given mean and standard deviation to z-scores using the formula: z = (x - mean) / standard deviation.

Next, look up the z-score in the standard normal distribution table to find the corresponding percentile. In this case, the z-score that corresponds to the 85th percentile is approximately 1.036.

Finally, use the formula x = (z * standard deviation) + mean to convert the z-score back to the original units. Plugging in the values, we get: x = (1.036 * 5) + 112. Therefore, the 85th percentile of Djokovic's first-serve speeds is approximately 117.18 mph.