# how do i find the formula?

A outdoor light bulb has an expected (mean) life of 8,000 hours with a standard deviation of 250 hours. How many bulbs in a batch of 500 can be expected to last no longer than 7500 hours?

• This website works better if you show us how far you got, where you got stuck, and so on. Mar 6 '14 at 6:19
• I just got to subtracting 7500 from 8000 and figured on 1st standard dev. and 2nd standard dev. but had no clue with what to do withe the # 500-thanks for your help
– Amy
Mar 7 '14 at 4:04
• OK, I think you are saying you worked out that 7500 hours is 2 standard deviations below the mean. Have you learned how to figure out what percentage of a sample is 2 or more standard deviations below the mean? Mar 7 '14 at 11:38

$$P(X<=7500) = P(z<=\frac{(7500-8000)}{250})$$
$$P(X<=7500) = P(z<=-2) = 0.02275$$
Expected number of bulbs in a batch of 500 that will not last longer than 7500 $$= .02275*500 = 12 bulbs$$