6) At the U.S. Open Tennis Championship a statistician keeps track of every serv

Question

6) 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 100 miles per hour (mph) and the standard deviation of the serve speeds was 8 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) 68 mph to 132 mph C) 76 mph to 124 mph B) 124 mph to 148 mph D) 84 mph to 116 mph 7) The amount of time workers spend commuting to their jobs each day in a large metropolitan city has a mean of 70 minutes and a standard deviation of 20 minutes. Assuming nothing is known about the shape of the distribution of commuting times, what percentage of these commuting times are between 30 and 110 minutes? A) at least 95% B) at least 89% C) at least 0% D) at least 75%

Explanation / Answer

6 Solution:- option C) 76 mph to 124mph

Because you don't know the shape of the distribution, the best you can do is use Chebyshev's rule.

Chebyshev's rule says no more than 1/k^2 of the distribution’s values can be more than k standard deviations away from the mean.

We want at least 88% in our interval, which means we want at most 12% outside that interval.

1/k^2 = .12

k^2 = 1/.12

k = sqrt(1/.12) = 2.88 = 3

Therefore, the interval 76 to 124 will contain at least 88% of the serves.

7 solution:-option D) at least 75%

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