SOLUTION: t a tennis tournament a statistician keeps track of every serve. The statistician reported that the mean serve speed of a particular player was 101 miles per hour (mph) and the st

Algebra ->  Test -> SOLUTION: t a tennis tournament a statistician keeps track of every serve. The statistician reported that the mean serve speed of a particular player was 101 miles per hour (mph) and the st      Log On


   

Question 1037363: t a tennis tournament a statistician keeps track of every serve. The statistician reported that the mean serve
speed of a particular player was 101 miles per hour (mph) and the standard deviation of the serve speeds was
14 mph. If nothing is known about the shape of the distribution, give an interval that will contain the speeds of
at least three-fourths of the player's serves.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
From Chebyshev's inequality,
P%28abs%28X+-+mu%29+%3C=+nd%29+%3E=+1-1%2Fn%5E2%29.
==> P%28abs%28X+-+101%29+%3C=+14n%29+%3E=+1-1%2Fn%5E2%29
Letting n = 2, we get
P%28abs%28X+-+101%29+%3C=+28%29+%3E=+1-1%2F2%5E2+=+1-1%2F4+=+3%2F4,
which is what is needed by the problem.
==> the interval is abs%28X+-+101%29+%3C=+28, or -28+%3C=+X+-+101+%3C=+28, or 73+%3C=+X+%3C=+128.