Please show work At the U.S. Open Tennis Championship a statistician keeps track

Question

Please show work

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 of a particular player was 98 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. 0 A. 143 mph to 188 mph B. 53 mph to 143 mph D. 68 mph to 128 mph

Explanation / Answer

If nothing is known about the distribution then we need to apply Chebychev's theorem which says that ateast (1 - 1/k^2) of the data lies between k standard deviations from the mean.

Hence,

(1 - 1/k^2) = 8/9

1/k^2 = 1/9

k = 3

Hence,

Interval that contains eight ninth of the player's serves

= (98 - 3*15) mph to (98 + 3*15) mph

= 53 mph to 143 mph

Option B is correct.

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