SOLUTION: A sample of the hourly wages of employees who work in a restaurant in Siem Reap has the mean of $5.02 and a standard deviation of $0.09. Using the Chebyshev's Theorem, find the ran

Algebra ->  Probability-and-statistics -> SOLUTION: A sample of the hourly wages of employees who work in a restaurant in Siem Reap has the mean of $5.02 and a standard deviation of $0.09. Using the Chebyshev's Theorem, find the ran      Log On


   

Question 1041007: A sample of the hourly wages of employees who work in a restaurant in Siem Reap has the mean of $5.02 and a standard deviation of $0.09. Using the Chebyshev's Theorem, find the range in which at least 75% of the date values fall.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Chebyshev's Theorem: P%28abs%28X+-+mu%29+%3C=+k%2Asigma%29+%3E=+1-1%2Fk%5E2
==> P%28abs%28X+-+5.02%29+%3C=+0.09k%29+%3E=+1-1%2Fk%5E2
Letting k = 2,
==> P%28abs%28X+-+5.02%29+%3C=+0.18%29+%3E=+1-1%2F2%5E2+=+3%2F4
==> P%28-0.18+%3C=+X+-+5.02+%3C=+0.18%29+%3E=+3%2F4
==> P%284.84+%3C=+X+%3C=+5.20%29+%3E=+3%2F4+=+0.75
==> the range in which at least 75% of the values fall is the interval
[4.84, 5.20].