At the us open tennis championship a statistician keeps track of every serve that a player hits during teh torunment. The statistcian reported that the mean serve speed of a particluar player was 101 miles per hour and teh standard deviation of the serve speeds was 11 mph. If nothing is known about the shape of distribution give an interval that will contain the speeds of at least eight ninths of the players serves

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adefunkeadewole adefunkeadewole · Answer 1 · 2020-10-14T03:59:26+02:00

Answer:

68mph to 134 mph

Step-by-step explanation:

We apply

Chebyshev's Theorem States:

At least 3/4 or 75% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.

At least 8/9 or 88.89% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

From the question,

Mean = 101 miles per hour

Standard deviation = 11 miles per hour

We are to give an interval that will contain the speeds of at least eight ninths of the players serves

Hence, we apply the rule

At least 8/9 or 88.89% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

μ - 3σ

= 101 - 3(11)

= 101 - 33

= 68 miles per hour

μ + 3σ.

= 101 + 3(11)

= 101 + 33

= 134 miles per hour

Therefore, the interval is 68mph to 134 mph