The amount of time a certain brand of light bulb lasts is normally distributed with a mean of 1200 hours and a standard deviation of hours. What is the probability that a randomly chosen light bulb will last more than 1280 hours, to the nearest thousandth?

Answer 1

To solve this problem, we first need to calculate the z-score for a light bulb lasting 1280 hours.

The z-score formula is:
z = (X - μ) / σ

where:
X = value we are interested in (1280 hours)
μ = mean (1200 hours)
σ = standard deviation (100 hours)

Plugging in the values:
z = (1280 - 1200) / 100
z = 80 / 100
z = 0.8

Next, we need to find the probability that a randomly chosen light bulb will last more than 1280 hours.

Using a z-table or z-score calculator, we can find that the probability corresponding to a z-score of 0.8 is approximately 0.7881.

Therefore, the probability that a randomly chosen light bulb will last more than 1280 hours is approximately 0.7881 or 78.81% (to the nearest thousandth).