SOLUTION: A new type of light bulb has an average lifespan of 1200 hours with a standard deviation of 75 hours Use the table to find out the probability that a lightbulb chosen at random wi

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Question 870607: A new type of light bulb has an average lifespan of 1200 hours with a standard deviation of 75 hours
Use the table to find out the probability that a lightbulb chosen at random will last 1140-1260 hours
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Convert the raw score of x = 1140 to a standard z-score

z = (x-mu)/sigma
z = (1140-1200)/75
z = -0.80


Now use this table to find the area to the left of z = -0.80

That area is 0.2119. Let's call this area1

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Convert the raw score of x = 1260 to a standard z-score

z = (x-mu)/sigma
z = (1260-1200)/75
z = 0.80



Now use this table to find the area to the left of z = 0.80

That area is 0.7881. Let's call this area2

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Now subtract the two areas:

Area2 - Area1 = 0.7881 - 0.2119 = 0.5762

The area between z = -0.80 and z = 0.80 is approximately 0.5762

So the area between x = 1140 and x = 1260 is also approximately 0.5762

That means the probability is about 0.5762 (roughly 57.62%)