SOLUTION: An electrical firm manufactures incandescent light bulbs that have a length of life (in hours) that is normally distributed. If the mean and standard deviation length of life of al

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Question 1171232: An electrical firm manufactures incandescent light bulbs that have a length of life (in hours) that is normally distributed. If the mean and standard deviation length of life of all lightbulbs produced are 1250 hours and 300 hours respectively, find the probability that a randomly selected bulb will last less than 1100 hours?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
use the online calculator at https://www.calculator.net/z-score-calculator.html to get p(x <= 1100) = .30854.

the z-score table i use can be found at https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf

this online calculator can find your answer directly from the raw score and the mean and the standard deviation without having to find the z-score first.

with the online calculator, you enter the raw score, the mean, and the standard deviation and the calculator tells you the area to the left of the raw score, the area to the right of the z-score.

since you want to know the probability of a score less than the raw score, you want the area to the left of the z-score.

you tell this calculator:
raw score = 1100
mean = 1250
standard deviation = 300
you click on calculator and the calculator tells you that the area to the left of the raw score is .30854.

here are the results from the calculator.

if you used the referenced table, you would first have to find the z-score and then use the table to find the area to the left of that z-score.

the z-score would be equal to (x - m) / sd = (1100 - 1250) / 300 = -150 / 300 = -.5

the z-score of -.5 would show an area to the left of it as .30854, same as you derived using the calculator.

here are the results from the table.