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!
Ok, my bad. I didn't read the question carefully enough.
You want the number that 97.5% of the bulbs last longer than.
That means you want the value corresponding to 100% - 97.5% = 2.5%
This is about 2 sigmas below the mean or 1200 - 2*50 = 1100 hrs.