Wilhelm McDermott
Feb 12, 2025
I really need some help with this statistics probability question?
I need assistance with a statistics probability question. A GE lightbulb is designed to last for 1,200 hours. However, the actual average lifespan of these lightbulbs is only 1,185 hours, with a standard deviation of 70 hours. What is the probability that a sample of 100 lightbulbs will have an average lifespan of at least 1,200 hours?
2 Answers
The distribution of GE lightbulb lifetimes follows the normal distribution with mean mu = 1185 and standard deviation sigma = 70.0. The lifetime value we’re interested in is x = 1200. The normalized z-score is
z = (1200-1185)/70.0 = 0.214285714286
and the probability that a GE lightbulb will last longer than 1200 hours
P(X>1200) = P(Z>0.21428571428571427) = 0.4151621288278977 = 1/2.41
that is, only about one in 2.5 GE lightbulbs, or 4 in 10, will last that long.
I’m surprised that an actual great corporation would be mentioned in a problem like this.
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