Assume the average age of an MBA student is 33.5 years old with a standard devia

Question

Assume the average age of an MBA student is 33.5 years old with a standard deviation of 2.1 years. Determine the coefficient of variation. Calculate the z-score for an MBA student who is 27 years old. Using the empirical rule, determine the range of ages that will include 99.7% of the students around the mean. Using Chebyshev's Theorem, determine the range of ages that will include at least 92% of the students around the mean. Using Chebyshev's Theorem, determine the range of ages that will include at least 83% of the students around the mean

Explanation / Answer

Coeff. of variation = SD / mean = 2.1 / 33.5

= 6.2687%

Z- score = 27 - 33.5 / 2.1

= -3.09

99.7% bounds:

Lower bound = 33.5 - 3(2.1) = 27.2 years

Upper bound = 33.5 + 3(2.1) = 39.8 years

Chebyshev: 92%

0.92 = 1 - 1/k2

Thus,

k = 3.5355

Thus age range = 33.5 +/- (3.5355 * 2.1)

= { 26.07 , 40.92}

Also,

Chebyshev: 83%

0.83 = 1 - 1/k2

Thus,

k = 2.4253

Thus age range = 33.5 +/- (2.4253 * 2.1)

= { 28.40 , 38.59}

Hope this helps.

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