The speed of college tennis player Jaron Jackson's first serve averages 125 mph, with a standard deviation of 4 mph.If the distribution of service speeds is normal, what proportion of Jaron's serves will be between 131 and 133 mph?
A).0035
B).044
C).0923
D).1087
E).036

Question

Quizplus · Accepted Answer

To find the proportion of Jaron's serves that fall between 131 and 133 mph, we use the Z-score formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. For 131 mph, Z = (131 - 125) / 4 = 1.5. For 133 mph, Z = (133 - 125) / 4 = 2. The proportion of serves between these Z-scores can be found using a standard normal distribution table or calculator. The difference in the cumulative probabilities for Z = 1.5 and Z = 2 gives approximately 0.044, indicating that about 4.4% of Jaron's serves are between 131 and 133 mph.

The Speed of College Tennis Player Jaron Jackson's First Serve