Answer to Question #313358 in Statistics and Probability for mae

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

We have a normal distribution, $\mu=120, \sigma=13, n=40.$

Let's convert it to the standard normal distribution,

$z=\cfrac{\bar{x}-\mu}{\sigma/\sqrt{n}}$ =

$=\cfrac{114-120}{13/\sqrt{40}}=-2.92,$

$P(\bar{X}>114)=1-P(\bar{X}<114)=\\ =1-P(Z<-2.92)=$

$=1-0.0018=0.9982$ ​(from z-table)