Suppose that quiz scores in a beginning statistics class have a mean of 7.2 with a standard deviation of 0.4. Using Chebyshev's Theorem, state the range in which at least 75% of the data will reside. Please do not round your answers.
Answer:
Given,
Mean = 7.2 , Standard deviation = 0.4
consider,
1 - 1/k^2 = 0.75
1/k^2 = 0.25
k^2 = 1/0.25
k^2 = 4
k = 2
Now consider,
Range = mean +/- 2*sd
= 7.2 +/- 2*0.4
= 7.2 +/- 0.8
= (6.4 , 8)
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