Question

The amount of time a certain brand of light bulb lasts is normally distributed with a mean of 1600 hours and a standard deviation of 20 hours. What percentage light bulbs last less than 1560 hours, to the nearest tenth?

Answer 1

To solve this problem, we need to use the standard normal distribution. We will first calculate the z-score for x = 1560:

z = (x - μ) / σ = (1560 - 1600) / 20 = -2

We then need to use a table or a calculator to find the area under the standard normal curve to the left of z = -2. Using a standard normal distribution table, we find that this area is approximately 0.0228.

Therefore, to the nearest tenth, approximately 2.3% of the light bulbs will last less than 1560 hours.