Answer to Question #311218 in Statistics and Probability for mima

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

The following are the population mean (μ)=120, population standard deviation (σ) =13 and sample size (n)=40

The corresponding z-value needed to be computed is:

$Z= \frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

=$\frac{114-120}{\frac{13}{\sqrt{40}}}$

=-2.92

$Pr( X ≥114)=P(Z\geq-2.92)$

=1-$P(Z\leq-2.92)$

=1-0.0018

=0.9982