Question

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 810 hours and a standard deviation of 92 hours. Find the probability that a random samples of 39 bulbs will have an average life of less than 783 hours

Answer 1

Let $X=$ the average life: $X\sim N(\mu, \sigma^2/n).$

Given $\mu=810\ h, \sigma=92\ h, n=39.$

$$P(X<783)=P(Z<\dfrac{783-810}{92/\sqrt{39}})$$

$$\approx P(Z<-1.832771)\approx0.0334$$