CHEBYSHEV'S THEOREM QUESTION

Question

Suppose that salaries for recent graduates of one university have a mean of $⁢25,500 with a standard deviation of $⁢1050. Using Chebyshev's Theorem, what is the minimum percentage of recent graduates who have salaries between $⁢22,350 and $⁢28,650? Round your answer to one decimal place.

Answer 1

at least 1-1/k^2 are within k standard deviations from the mean

sd = 1050, mean = 25500

what percent are between 22,350 and 28,650??

z = 28650- 25500)/1050 = 3150/1050= 315/105= 3

by the empirical rule 99.7% are within 3 sd's of the mean

2nd z = (22350 -25500)/1050 = - 3150/1050 = -3

99.7% are between $22,350 and $26500