Answer:
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:
<u><em>Step(i):-</em></u>
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
<u><em>Step(ii):- </em></u>
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
<u><em>Final answer:-</em></u>
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%