Question

Please show all your work.

4 Light Bulbs The lifetimes of light bulbs produced by a c mean 1000 hours and standard deviation 100 hours. ompany are independent and normally distributed with (a) What is the probability that a bulb will last less than 800 hours? (b) What is the probability that a bulb will last at least 1200 hours? (c) If 2 new bulbs are installed at the same time, what is the probability that they will both still be burning after 1200 hours?

Answer 1

Given that X follows a Normal distribution with Mean = mu = 1000 S.D = sigma = 100 Note that z = (x - mu)/sigma = (x - 1000)/100 ...(Eq.1) follows standard Normal. (a) When x = 800, from (Eq.1), z = -2 P (X < 800) = P (Z < - 2) = 0.0228 (ans) (b) When x = 1200, from (Eq.1), z = 2 P (X > 1200) = P (Z > 2) = 1- P (Z < 2) = 1 - 0.9772 = 0.0228 (ans) (c) Probability = 2 P (X > 1200) = 2 times 0.0228 = 0.0456 (ans)