Question

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 813 hours and a standard deviation of 65 hours. Find the probability that a random samples of 34 bulbs will have an average life of greater than 803 hours.

Answer 1

$P(\bar X>803)=P(Z>\frac{803-813}{\frac{65}{\sqrt{34}}})=P(Z>-0.90)=1-P(Z<-0.90)=0.8159.$