Question

Light bulbs are installed successively into a socket. If we assume that each light bulb has a mean life of 2 months with a standard deviation of 0.25 months, what is the probability that 40 bulbs last at least 7 years?

(a) 0.001
(b) 0.005
(c) 0.010
(d) 0.015

Answer 1

The probability that 40 bulbs last at least 7 years is 1.

Step-by-step explanation:

To find the probability that 40 bulbs last at least 7 years, we need to calculate the probability that a single bulb lasts at least 7 years and then raise it to the power of 40. The mean life of a light bulb is 2 months, which is equal to 1/6 of a year. So, the probability that a single bulb lasts at least 7 years or 42 months is:

P(X ≥ 42) = 1 - P(X < 42) = 1 - P(Z < (42 - 40)/0.25) = 1 - P(Z < 8)

This probability can be calculated using a standard normal distribution table or a calculator to find the area to the left of 8, which is approximately 1. The probability that all 40 bulbs last at least 7 years is:

P(X ≥ 42)^{40} = 1^{40} = 1

So, the probability that 40 bulbs last at least 7 years is 1, which is not one of the given options (a)-(d).