1. ## 68-95-99.7 Rule Help

A company produces lightbulbs. The lifetimes (in hours) of lightbulbs have a normal distribution with a mean of 1200 hours and a standard deviation of 50 hours. Use the 68-95-99.7 rule to answer the following questions:

(a) 84% of the lightbulbs burn out before how many hours?
(b) 0.15% of the lightbulbs burn out before how many hours?
(c) 97.5% of the lightbulbs last longer than how many hours?

My Attempt: (Using the mean - sigma equation)
(a) 1200 - 2 * 50 = 1100 hours
(b) 1200 - 3 * 50 = 1050 hours
(c) 1200 + 3 * 50 = 1350 hours

I don't think I did this right but if someone could explain to me how to solve this problem I would be very thankful!

2. ## Re: 68-95-99.7 Rule Help

Originally Posted by michellederz
A company produces lightbulbs. The lifetimes (in hours) of lightbulbs have a normal distribution with a mean of 1200 hours and a standard deviation of 50 hours. Use the 68-95-99.7 rule to answer the following questions:

(a) 84% of the lightbulbs burn out before how many hours?
(b) 0.15% of the lightbulbs burn out before how many hours?
(c) 97.5% of the lightbulbs last longer than how many hours?

My Attempt: (Using the mean - sigma equation)
(a) 1200 - 2 * 50 = 1100 hours
(b) 1200 - 3 * 50 = 1050 hours
(c) 1200 + 3 * 50 = 1350 hours

I don't think I did this right but if someone could explain to me how to solve this problem I would be very thankful!
a) 84% is 1 sigma above the mean. This would be 1200 + 50 = 1250 hrs.

b) 0.15% is 3 sigmas below the mean, i.e. 1200 - 3*50 = 1050 hrs, you did this correctly

c) 97.5% is about 2 sigmas above the mean i.e. 1300 hrs

3. ## Re: 68-95-99.7 Rule Help

Originally Posted by romsek
a) 84% is 1 sigma above the mean. This would be 1200 + 50 = 1250 hrs.

b) 0.15% is 3 sigmas below the mean, i.e. 1200 - 3*50 = 1050 hrs, you did this correctly

c) 97.5% is about 2 sigmas above the mean i.e. 1300 hrs
Oh! This makes sense.
So when I create the graph, will I shade in 85% of the area to the right or left of the mean for part a? I shaded in coming from the left side of the graph and it goes 1 standard deviation over the mean. Is this correct?

4. ## Re: 68-95-99.7 Rule Help

the blue area is what you want.

5. ## Re: 68-95-99.7 Rule Help

Originally Posted by romsek

the blue area is what you want.
Perfect, that is what I have down. However, I believe part c is wrong. Could it possibly be 1350? I asked my professor if 1300 was right and he told me no but will not tell me why.