Question

A company installs 5,000 light bulbs. The lifetimes of the lightbulbs are approximately normally distributed with a mean of 500 hours and a standard deviation of 100 hours. Find the approximate number of bulbs that can be expected to last the indicated amount of time.

At least 500 hours

A) 2,500
B) 1,000
C) 2,400
D) 5,000

Answer 1

Approximately 2,500 out of 5,000 light bulbs are expected to last at least 500 hours since 50% of the normally distributed lifetimes are above the mean, which is equal to 500 hours.

Step-by-step explanation:

The question is asking to determine the number of light bulbs expected to last at least 500 hours. We are given that the lifetimes of the light bulbs are normally distributed with a mean of 500 hours and a standard deviation of 100 hours.

To find the number of bulbs that will last at least 500 hours, we look at the normal distribution curve. The mean of the distribution is 500, so we can expect that 50% of the values will be above the mean. Since there are 5,000 light bulbs in total, we can expect that approximately 50% of them, or 2,500 light bulbs, will last at least 500 hours. Therefore, the answer is (A) 2,500.