Answer to Question #304942 in Statistics and Probability for aecee0514

Question #304942

An electronic company in Laguna manufactures resistors that have a mean resistance of 120 ohms and a standard deviation of 13 ohms. Find the probability that a random sample of 40 resistors will have an average resistance greater than 114 ohms.


1
Expert's answer
2022-03-03T09:49:23-0500

Let X=X= an average resistance: XN(μ,σ2/n).X\sim N(\mu, \sigma^2/n).

Given μ=120Ω,σ=13Ω,n=40.\mu=120\Omega, \sigma=13\Omega , n=40.


P(X>114)=P(Z>11412013/40)P(X>114)=P(Z>\dfrac{114-120}{13/\sqrt{40}})

P(Z>2.9190)0.9982\approx P(Z>-2.9190)\approx0.9982


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