Question

5.   The University of Pennsylvania randomly decided to assess its student population as they prepared for an audit by the federal government.  In the Liberal Arts division, they found that the average age was 31.6years old with a standard deviation of 2.8 years.

a.    Determine the coefficient of variation.

b.   Calculate the z-score for a Liberal Arts student who is 28 years old.

c.   Use the Empirical Rule to identify the range in ages that will include 997% of the students around the mean.

d.   Use Chebyshev’s theorem to determine the range in ages that will include at least 94% of the students around the mean.

Answer 1

a.    Determine the coefficient of variation.

CV = %

b.   Calculate the z-score for a Liberal Arts student who is 28 years old.

z-score =

c.   Use the Empirical Rule to identify the range in ages that will include 997% of the students around the mean.

(31.6 - 3*2.8, 31.6 + 3*2.8)

(23.2, 40)

d.   Use Chebyshev’s theorem to determine the range in ages that will include at least 94% of the students around the mean.

1 - 1/k² 0.94

k = 4.08

(31.6 - 4.08*2.8, 31.6 + 4.08*2.8)

(20.17, 43.03)