Question

At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. If nothing is known about the shape of the distribution, what percentage of the player's serve speeds are less than 70 mph?

Answer 1

2.275%

Explanation:

We solve this question using z score formula

z = (x-μ)/σ,

where

x is the raw score = 70 mph

μ is the population mean = 100 mph

σ is the population standard deviation = 15 mph

z score = 70 - 100/15

z score = -30/15

z score = - 2

Determining the Probability value from Z-Table:

P(x ≤ 70) = P(x < 70)

= P(z = -2)

= 0.02275

Hence the probability of the player's serve that are less than 70 mph is 0.02275

Converting it to percentage

= 0.02275 × 100

= 2.275%

Therefore, the percentage of the player's serve speeds that are less than 70 mph is = 2.275%