Question

One of the biggest strengths in any tennis player’s game is their serve. While the best tennis players use a combination of power and precision in their serves, sports statistics have shown that players with faster serve speeds are generally more successful in tournament play.Assume that in men’s professional tennis, the speed of first serves is approximately normally distributed with a mean of 120.8 mph and a standard deviation of 4.4 mph.Assume that in women’s professional tennis, the speed of first serves is approximately normally distributed with a mean of 104 mph and a standard deviation of 5.32 mph. What proportion of first serves of players in the men’s tournament have a speed faster than 119.1 mph?

Answer 1

To find the proportion of first serves in the men’s tournament that have a speed faster than 119.1 mph, calculate the z-score and find the corresponding proportion in the standard normal distribution. The proportion is approximately 0.35, or 35%.

Step-by-step explanation:

To find the proportion of first serves in the men’s tournament that have a speed faster than 119.1 mph, we need to calculate the z-score and then find the corresponding proportion in the standard normal distribution.

First, we calculate the z-score using the formula: z = (x - mean) / standard deviation.

Plugging in the values, we get: z = (119.1 - 120.8) / 4.4 = -0.3864.

Next, we look up the corresponding proportion using a z-table or calculator. The proportion of first serves with a speed faster than 119.1 mph is approximately 0.35, or 35%.