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 1100 hours?
A) 0.4772
B) 0.9772
C) 0.0228
D) 0.5228
E) 0.5513

Question

Quizplus · Accepted Answer

To solve the problem, we need to use the standard normal distribution since we are given the mean and standard deviation of the population. We can convert the given values into z-scores using the formula:

z = (x - μ) / σ

where x is the value we are interested in (in this case, 1100 hours), μ is the mean (1000 hours), and σ is the standard deviation (50 hours).

z = (1100 - 1000) / 50 = 2

We can then look up the area to the left of z = 2 in the standard normal distribution table (or use a calculator or software). The area is 0.9772.

Therefore, the probability that a randomly selected bulb would last fewer than 1100 hours is 0.9772 or approximately 98%.

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