Respuesta :
Answer:
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
P(X>364.8) = 0.6844
Step-by-step explanation:
Step(i):-
Given mean of the Population = 364 watts
Given standard deviation of the Population = 12 watts
Let 'X ' be the Random variable in Normal distribution
x⁻ = 364.8
Given sample size 'n' = 52
[tex]Z = \frac{x-mean}{S.E}[/tex]
Standard error (S.E) = σ/√n = 1.664
[tex]Z = \frac{364.8-364}{1.664}[/tex]
Z = 0.481
Step(ii):-
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
P(X>364.8) = P(Z>0.481)
= 1- P( Z<0.481)
= 1- (0.5 -A(0.481)
= 0.5 + A(0.481)
= 0.5 + 0.1844
= 0.6844
Final answer:-
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
P(X>364.8) = 0.6844
