Light bulbs are normally distributed with an average lifetime of 1000 hours and a standard deviation of 250 hours. The probability that a light bulb picked at random will last less than 1500 hours is about:
A)97.72 percent.
B)95.44 percent.
C)75.00 percent.
D)68.00 percent.

Question

Quizplus · Accepted Answer

To find the probability that a light bulb will last less than 1500 hours, we use the Z-score formula: Z = (X - μ) / σ, where X is the value (1500 hours), μ is the mean (1000 hours), and σ is the standard deviation (250 hours). Plugging in the values, we get Z = (1500 - 1000) / 250 = 500 / 250 = 2. A Z-score of 2 corresponds to approximately 97.72% of the distribution lying below this value, according to the standard normal distribution table.

Light Bulbs Are Normally Distributed with an Average Lifetime of 1000