Answer to Question #296064 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 810 hours and a standard deviation of 74 hours. Find the probability that a random samples of 36 bulbs will have an average life of greater than 803 hours

Answer 1

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

Given $\mu=810\ h, \sigma=74\ h, n=36.$

$$P(X>803)=1-P(X\le 803)$$

$$=1-P(Z\le \dfrac{803-810}{74/\sqrt{36}})$$

$$\approx 1-P(Z\le-0.567568)$$

$$\approx0.714836$$