Assume the average age of an MBA student is 31.3 years old with a standard devia

Question

Assume the average age of an MBA student is 31.3 years old with a standard deviation of 2.6 years. a) Determine the coefficient of variation. b) Calculate the z-score for an MBA student who is 29 years old. c)Using the empirical rule, determine the range of ages that will include 95% of the students around the mean. d)Using Chebyshev's Theorem, determine the range of ages that will include at least 92% of the students around the mean. e) Using Chebyshev's Theorem, determine the range of ages that will include at least 81% of the students around the mean.

Explanation / Answer

a) CV = coefficient of variation is a measure of spread that describes the amount of variability relative to the mean

= 2.6/31.3 *100= 8.306%

b)

Z= 29-31.3/2.6

= -.885

c) 3 stdev is 95% which means 31.3+/0 3*2.6 = 31.3 +/- 7.8

d)

1-1/k^2 = .92

k^2 = 1/.08 = 100/8 =12.5

k = sqrt(12.5) = 3.56

So range of ages is 31.3+/- 3.56*2.6

e) 1-1/k^2 = .81

k^2 = 1/.19 = 5.26

k = sqrt(5.26) = 2.295

So range of ages is 31.3+/- 2.295*2.6

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