The heights of the adults in one town have a mean of 67.1 inches and a standard deviation of 3.5 inches. What can you conclude from Chebyshev's theorem about the percentage of adults in the town whose heights are between 60.1 and 74.1 inches?

The percentage of adults in the town whose heights are between 60.1 and 74.1​ inches

P( 60.1≤X≤74.1) = 2.26 %

Step-by-step explanation:

Step(i):-

Given that the heights of the adults in one town have a mean of 67.1 inches

Mean of the Population = 67.1 inches

The standard deviation of the Population = 3.5inches

Let X₁ =60.1

Let X₂ = 74.1

Step(ii):-

The probability of adults in the town whose heights are between 60.1 and 74.1​ inches

P( X₁ ≤X≤X₂) = P(Z₁≤Z≤Z₂)

                    = P( -2≤ Z≤-4)

                   = |A(-4) -A(-2)|

                   = A(4) - A(2)|     (∵ A(-Z) =A(Z))

                  = 0.4998 - 0.4772

                 = 0.0226

Final -

The probability of adults in the town whose heights are between 60.1 and 74.1​ inches

P( X₁ ≤X≤X₂) = 0.0226

The percentage of adults in the town whose heights are between 60.1 and 74.1​ inches

P( 60.1≤X≤74.1) = 2.26%

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