Analysis of Rafael Nadal's Serve Speed and Growth Distribution of Three-Year-Old Females

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This report analyzes the first serve speeds of Rafael Nadal during the 2008 Wimbledon tournament, where his serves averaged 115 mph with a standard deviation of 6 mph. Using the properties of the normal distribution, we will calculate the proportion of serves expected to exceed 120 mph. Additionally, we explore the heights of three-year-old females, which are normally distributed with a mean of 94.5 cm and a standard deviation of 4 cm, and determine the third quartile of this distribution.

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Jan 20, 2026

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Analysis of Rafael Nadal's Serve Speed and Growth Distribution of Three-Year-Old Females

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In the 2008 Wimbledon tennis tournament, Rafael Nadal averaged 115 miles per hour on his first serves. Assume that the distribution of his first-serve speeds in normal with a mean of 115 mph and a standard deviation of 6 mph. About what proportion of his first serves would you expect to exceed 120 mph?
According to the cdc.gov growth charts, the heights of three-year-old females are approximately Normally distributed with a mean of 94.5 cm and a standard deviation of 4 cm. What is the third quartile of this distribution?

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