Answer to Question #304942 in Statistics and Probability for aecee0514

Question

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.

Answer 1

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

Given $\mu=120\Omega, \sigma=13\Omega , n=40.$

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

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