Question

At the Canada 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 of a particular player was 99 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, give an interval that will contain the speeds of at least eight-ninths of the player's serves.

a) 54 mph to 144 mph
b) 39 mph to 159 mph
c) 144 mph to 189 mph
d) 69 mph to 129 mph

Answer 1

a) 54 mph to 144 mph

Explanation:

We don't know the shape of the distribution, so we use Chebyshev's Theorem to solve this question. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

At least eight-ninths of the player's serves.

8/9 is approximately 89%

So

Mean: 99, standard deviation: 15

99 - 3*15 = 54

99 + 3*15 = 144

So the correct answer is:

a) 54 mph to 144 mph