The expected (mean)life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours.The life of this bulb is normally distributed.Which most closely reflects the probability that a randomly selected bulb would last longer than 1150 hours?
A)0.4987
B)0.9987
C)0.0013
D)0.5013
E)0.5513

Question

Quizplus · Accepted Answer

To find the probability that a bulb lasts longer than 1150 hours, we use the Z-score formula: Z = (X - μ) / σ, where X is the value in question, μ is the mean, and σ is the standard deviation. Here, Z = (1150 - 1000) / 50 = 3. A Z-score of 3 corresponds to a probability of 0.9987 in the standard normal distribution for values less than 1150 hours, meaning the probability for more than 1150 hours is 1 - 0.9987 = 0.0013.

The Expected (Mean)life of a Particular Type of Light Bulb