Question

17. The life of light bulbs is distributed normally. The variance of the lifetime is 225 and the mean lifetime of a bulb is 590 hours. Find the probability of a bulb lasting for at most 600 hours. Round your answer to four decimal places.

18. Find the area under the standard normal curve to the left of z=2.63. Round your answer to four decimal places, if necessary.

Answer 1

Solution: We are life of light bulbs is normally distributed with mean and variance .

Therefore, we have:

Find the probability of a bulb lasting for at most 600 hours.

Let x be the number of hours a bulb lasts. Therefore, we have to find

First we need to find the z score corresponding to

Therefore, we have to find . Using the standard normal table, we have:

Therefore, the probability of a bulb lasting for at most 600 hours is

18. Find the area under the standard normal curve to the left of z=2.63.

Answer: Here we have to find .

Using the standard normal table, we can find the area to the left of 2.63. Therefore, we have:

Therefore, the area under the standard normal curve to the left of z=2.63 is