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 fewer than 940 hours?
A)0.3849
B)0.8849
C)0.1151
D)0.6151
E)0.6563

Question

Quizplus · Accepted Answer

To find the probability that a bulb lasts fewer than 940 hours, we calculate the Z-score using the formula Z = (X - μ) / σ, where X is the value of interest (940 hours), μ is the mean (1000 hours), and σ is the standard deviation (50 hours). Plugging in the values, we get Z = (940 - 1000) / 50 = -60 / 50 = -1.2. Looking up the Z-score of -1.2 in a standard normal distribution table or using a calculator, we find the probability associated with a Z-score of -1.2 is approximately 0.1151. This means there's about an 11.51% chance a randomly selected bulb will last fewer than 940 hours.

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