A dusk to dawn outdoor lightbulb 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 7,500 hours?

the answer is 11.5 bulbs.

basically what you have to do is since you know one standard deviation is 250 hours, then 2 standard deviations is 500 hours (which is the difference between the mean of 8000 hours and the percent of bulbs lasting only 7500 hours). the standard deviation is -2 because the bulb last shorter than the mean. you then add up all the percentages to the left of the z-score -2 which comes out to 2.3%. now you multiply 500 (total bulbs) by .023 (23%) and you get 11.5 bulbs

Step-by-step explanation:

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δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)

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step-by-step explanation: