Question

Assume the average age of an MBA student is 31.3 years old with a standard deviation of 2.3 years.

​a) Determine the coefficient of variation.

​b) Calculate the​ z-score for an MBA student who is 28 years old.

​c) Using the empirical​ rule, determine the range of ages that will include 99.7% of the students around the mean.

​d) Using​ Chebyshev's Theorem, determine the range of ages that will include at least 93% of the students around the mean.

​e) Using​ Chebyshev's Theorem, determine the range of ages that will include at least 78​% of the students around the mean.

Answer 1

a)coefficient of variation =(std deviation/mean)=(2.3/31.3)=0.0735 ~ 7.35%

b)z score=(X-mean)/std deviation=(28-31.3)/2.3=-1.43

c)as we know that 99.7% values are 3 std deviation from mean

hence range of data=31.3-/+3*2.3=24.4 to 38.2

d)for % of values k std deviation from mean as per Chebychev's theorum=(1-1/k²)=0.93

hence k=sqrt(1/(1-0.93))=3.78

therefore range =31.3-/+3.78*2.3=22.61 ; 39.99

e)

k=sqrt(1/(1-0.78))=2.13

therefore range =31.3-/+2.13*2.3=26.40 ; 36.20