Answer:
<em>The probability that the mean amplifier output would be greater than 364.8 watts in a sample of 52 amplifiers if the claim is true</em>
<em>P(X>364.8) = 0.6844</em>
Step-by-step explanation:
<u><em>Step(i):-</em></u>
<em>Given mean of the Population = 364 watts</em>
<em>Given standard deviation of the Population = 12 watts</em>
<em>Let 'X ' be the Random variable in Normal distribution </em>
<em>x⁻ = 364.8</em>
<em>Given sample size 'n' = 52 </em>
<em /><em />
<em>Standard error (S.E) = σ/√n = 1.664</em>
<em /><em />
Z = 0.481
<u><em>Step(ii):-</em></u>
<em>The probability that the mean amplifier output would be greater than 364.8 watts in a sample of 52 amplifiers if the claim is true</em>
<em>P(X>364.8) = P(Z>0.481)</em>
<em> = 1- P( Z<0.481)</em>
= 1- (0.5 -A(0.481)
= 0.5 + A(0.481)
= 0.5 + 0.1844
= 0.6844
<u><em>Final answer:-</em></u>
<em>The probability that the mean amplifier output would be greater than 364.8 watts in a sample of 52 amplifiers if the claim is true</em>
<em>P(X>364.8) = 0.6844</em>
<em />
<em />