A data set has a mean of 1,600 and a standard deviation of 120. Using Chebyshev\

Question

A data set has a mean of 1,600 and a standard deviation of 120.

Using Chebyshev's theorem, what percentage of the observations fall between 1,240 and 1,960? (Do not round intermediate calculations. Round your answer to the nearest whole percent.)

Using Chebyshev’s theorem, what percentage of the observations fall between 1,360 and 1,840? (Do not round intermediate calculations. Round your answer to the nearest whole percent.)

Using Chebyshev's theorem, what percentage of the observations fall between 1,240 and 1,960? (Do not round intermediate calculations. Round your answer to the nearest whole percent.)

Explanation / Answer

A) MEAN = 1600, STANDARD DEVIATION = 120

P(1240<X<1960)

Z SCORE (1240 - 1600) /120 = -3

Z SCORE = (1960- 1600)/120 = +3

NOW

1 - (1/k)^2 percent of the observations fall between k standard deviations.

HERE K = 3

HENCE ANSWER = 1 - (1/3)^3 = 88.8

B) P(1360<X<1840)

Z SCORE = (1360- 1600)/120 = -2

Z SCORE = (1840 - 1600) /120 = 2

HENCE HERE K = 2

1 - (1/k)^2 percent of the observations fall between k standard deviations.

THEREFORE 1 - (1/2)^2

= 75%

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