The expected (mean)life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours.The life of this bulb is normally distributed. What is the probability that a randomly selected bulb would last fewer than 940 hours?
A) 0.3849
B) 0.8849
C) 0.1151
D) 0.6151
E) 0.6563

Question

Quizplus · Accepted Answer

We need to find the probability that a randomly selected bulb would last fewer than 940 hours, which can be written mathematically as P(X<940), where X is the random variable denoting the life of a bulb. Since the life of the bulb is normally distributed with a mean (µ) of 1,000 hours and a standard deviation (σ) of 50 hours, we can standardize our variable using the z-score formula:
z = (X - µ) / σ
z = (940 - 1000) / 50
z = -1.2
Now we need to find the probability corresponding to this z-score from the standard normal distribution table (or calculator), which is P(Z < -1.2) = 0.1151. Therefore, the probability that a randomly selected bulb would last fewer than 940 hours is 0.1151 or 11.51%, which corresponds to option C.

The Expected (Mean)life of a Particular Type of Light Bulb