Answer:
<em>The probability of the length of a randomly selected Cane being between 360 and 370 cm P(360 ≤X≤370) = 0.6851</em>
Step-by-step explanation:
<u>step(i)</u>:-
<em>Let 'X' be the random Normal variable</em>
<em>mean of the Population = 365.45</em>
<em>Standard deviation of the population = 4.9 cm</em>
<em>Let X₁ = 360</em>
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<em>Z₁ = -1.112</em>
<em>Let X₂ = 370</em>
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<em>Z₂ = 0.911</em>
<u><em>Step(ii</em></u><em>):-</em>
<em>The probability of the length of a randomly selected Cane being between 360 and 370 cm</em>
<em> P(x₁≤x≤x₂) = P(z₁≤Z≤z₂) </em>
<em> P(360 ≤X≤370) = P(-1.11≤Z≤0.911)</em>
<em> = P(Z≤0.911)-P(Z≤-1.11)</em>
<em> = 0.5 +A(0.911) - (0.5-A(1.11)</em>
<em> = 0.5 +A(0.911) - 0.5+A(1.11)</em>
<em> = A(0.911) + A(1.11)</em>
<em> = 0.3186 + 0.3665</em>
<em> = 0.6851</em>
<em>The probability of the length of a randomly selected Cane being between 360 and 370 cm P(360 ≤X≤370) = 0.6851</em>
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