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 60 hours. What percentage light bulbs last less than 1160 hours, to the nearest tenth?

1 answer

To find the percentage of light bulbs that last less than 1160 hours, we need to first calculate the z-score for 1160 hours using the z-score formula:

z = (X - μ) / σ

where X = 1160 hours, μ = 1200 hours, and σ = 60 hours.

z = (1160 - 1200) / 60
z = -40 / 60
z = -0.67

Next, we can use a standard normal distribution table or a calculator to find the percentage of values below z = -0.67.

From the standard normal distribution table, the percentage is approximately 25.5%.

Therefore, approximately 25.5% of light bulbs last less than 1160 hours.