Empirical Rule problem

Hello everyone,

I'm taking another statistics class, and I'm already a bit rusty on the first one I took (which was only about 6 months ago) but anything math oriented is really not my strong point. I'm trying to look back at my old book and in my new one to figure this problem out:

The manufacturer of an extended-life lightbulb claims the bulb has an average life of 12,000 hours, with a standard deviation of 500 hours. If the distribution is bell shaped and symmetrical, what is the approximate percentage of these bulbs that will last

a. between 11,000 and 13,000 hours?
b. over 12,500 hours?
c. less than 11,000 hours?
d. between 11,500 and 13,000 hours?

I am going by the normal curve and following a picture with the percentages in my original stats book to arrive at my answers:

a. 95%
b. 81.5%
c. 2.35%
d. 83.85%

I have a feeling I might be trying to oversimplify the process, so I believe at least a couple of these answers are wrong. Can anyone help out with some refresher info or other input? It would be much appreciated!

Flora

M = 12,000
? = 500

For x < M-3?
x < 10,500 ? 0.15%

For M-3? < x < M-2?
10,500 < x < 11,000 ? 2.35%

For M-2? < x < M-?
11,000 < x < 11,500 ? 13.5%

For M-? < x < M
11,500 < x < 12,000 ? 34%

For M < x < M+?
12,000 < x < 12,500 ? 34%

For M+? < x < M+2?
12,500 < x < 13,000 ? 13.5%

For M+2? < x < M+3?
13,000 < x < 13,500 ? 2.35%

For x > M+3?
x > 13,500 ? 0.15%

Thank you Loren. Here are my revised answers. Would anyone mind confirming if they are accurate?

a. 95%
b. 15.85%
c. 2.35%
d. 81.5%


Flora