Answer:
<em>The probability that the mean of this sample of home purchases is between 173 and 174 homes</em>
<em>P(173≤X≤174) = 0.0936</em>
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given that the mean of the Population = 175
Given that the standard deviation of the Population = 6
Let 'x⁻' be the mean of the random sample
Given that x₁⁻ = 173
Given that x₂⁻ = 174
<u><em>Step(ii):-</em></u>
<u><em>The probability that the mean of this sample of home purchases is between 173 and 174 homes</em></u>
<em>P(X₁≤X≤X₂) = P(Z₁≤Z≤Z₂)</em>
<em> = P(Z≤Z₂) - P(Z≤Z₂) ( both values 'Z' values are negative)</em>
<em> = 0.5 -A(Z₁) - (0.5 -A(Z₂))</em>
<em> = |A(Z₂) -A(Z₁)|</em>
<em>P(173≤X≤174) = | A(2.58)-A(1.29)|</em>
<em> = 0.4951 - 0.4015 (∵ from normal table)</em>
<em> = 0.0936</em>
<u><em>Final answer:-</em></u>
<em>The probability that the mean of this sample of home purchases is between 173 and 174 homes</em>
<em>P(173≤X≤174) = 0.0936</em>
<em> </em>