Answer to Question #311221 in Statistics and Probability for ygfit

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

Solution

Population mean $\mu=120$

Population standard deviation $\sigma=13$

$Z=\dfrac{X-\mu}{\sigma}=\dfrac{114-120}{13}$

$Z=-2$

From normal distribution tables

$P(Z of -2) =0.02275$

Probability that the sample mean $\bar X$ is greater than 114 is;

$=1-0.02275$

$=0.97725$