Question

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 811 hours and a standard deviation of 95 hours. Find the probability that a random samples of 44 bulbs will have an average life of less than 799 hours.

Answer 1

$\mu=811\\\sigma=95\\n=44$

Let $X$ denote the length of life of light bulbs.

We find,

$p(x\lt 799)=p(Z\lt{799-811\over{95\over\sqrt{44}}})=p(Z\lt-0.84)=\phi(-0.84)=0.2005$

Therefore, the probability that a random sample of 44 bulbs will have an average life of less than 799 hours is 0.2005.