Question

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 800 hours and a standard deviation of 65 hours. Find the probability that a random samples of 46 bulbs will have an average life of less than 788 hours.

Answer 1

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

Given $\mu=800\ h, \sigma=65\ h, n=46.$

$$P(X<788)=P(Z<\dfrac{788-800}{65/\sqrt{46}})$$

$$\approx P(Z<-1.252122)\approx0.105263$$