Question

A data set has a mean of 1500 and a standard deviation of 100.

a. Using Chebyshev's theorem, what percentage of the observations fall between 1300 and 1700? (Do not round intermediate calculations. Round your answer to the nearest whole percent.)

b. Using Chebyshev’s theorem, what percentage of the observations fall between 1200 and 1800? (Do not round intermediate calculations. Round your answer to the nearest whole percent.)

Answer 1

Solution:

Given, the distribution have

mean = 1500 and SD = 100

According to Chebyshevs Theorem ,  

P[( - k) < X < ( + k) ] =  

a)

1300 = 1500 - (2 * 100) = - 2

1700 = 1500 + (2 * 100) = + 2

So , here k = 2

= 1 - (1/2² ) = 0.75 = 75%

Answer : 75%

b)

Here . k = 3

= 1 - (1/3² ) = 0.89 = 89%

Answer: 89%