Answer:
<em>The probability that the mean of my sample will be between 24 and 25 cm</em>
<em>P(24 ≤X⁻≤25) = 0.4772</em>
Step-by-step explanation:
<u><em>Step(i)</em></u>:-
<em>Given mean of the Population 'μ'= 25c.m</em>
<em>Given standard deviation of the Population 'σ' = 8c.m</em>
<em>Given sample size 'n' = 256</em>
<em>Let X₁ = 24</em>
<em></em><em></em>
<em>Let X₂ = 25</em>
<em></em><em></em>
<u><em>Step(ii)</em></u><em>:-</em>
<em>The probability that the mean of my sample will be between 24 and 25 cm</em>
<em>P(24 ≤X⁻≤25) = P(-2≤ Z ≤0)</em>
= P( Z≤0) - P(Z≤-2)
= 0.5 + A(0) - (0.5- A(-2))
= A(0) + A(2) ( ∵A(-2) =A(2)
= 0.000+ 0.4772
= 0.4772
<u><em>Final answer</em></u>:-
<em>The probability that the mean of my sample will be between 24 and 25 cm</em>
<em>P(24 ≤X⁻≤25) = 0.4772</em>