Answer to Question #292069 in Statistics and Probability for secret

Question

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 780 hours and a standard deviation of 89 hours. Find the probability that a random samples of 31 bulbs will have an average life of greater than 814 hours.An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 780 hours and a standard deviation of 89 hours. Find the probability that a random samples of 31 bulbs will have an average life of greater than 814 hours.

Answer 1

$n=31\\\sigma=89\\\mu=780$

We are required to find the probability, $p(\bar x\gt 814)=p(Z\gt{814-\mu\over{\sigma\over\sqrt{n}}})=p(Z\gt{814-780\over{89\over\sqrt{31}}})=p(Z\gt 2.13)$

This is equivalent to,

$p(Z\gt 2.13)=1- p(Z\lt 2.13)=1-0.9834=0.0166$.

Therefore, the probability that a random sample of 31 bulbs will have an average life greater than 814 hours is 0.0166.