Question

An electrical company claims that the average life of the bulbs it manufactures is 1 100 hours with a standard deviation of 200 hours. If a random sample of 110 bulbs is chosen, what is the probability that the sample mean will be between 1120 hours and 1 150 hours?

Answer 1

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

Given $\mu=1100h, \sigma=200h, n=110.$

$$P(1120<X<1150)=P(Z<\dfrac{1150-1100}{200/\sqrt{110}})$$

$$-P(Z\le\dfrac{1120-1100}{200/\sqrt{110}})$$

$$\approx P(Z<2.6220)-P(Z\le1.0488)$$

$$\approx0.99563-0.85286=0.1428$$