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?Group of answer choicesapproximately 2.5%at most 12.5%at most 11%at most 25%
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?Group of answer choicesapproximately 2.5%at most 12.5%at most 11%at most 25%
Solution
To answer this question, we need to use the empirical rule (also known as the 68-95-99.7 rule) which applies to a normal distribution. However, the question states that "nothing is known about the shape of the distribution", which means we cannot assume it's a normal distribution and therefore we cannot use the empirical rule.
So, without knowing the shape of the distribution, we cannot accurately determine the percentage of the player's serve speeds that are less than 70 mph. None of the provided answer choices can be definitively chosen based on the information given.
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