If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, approximately what percentage of light bulbs has a life of more than 3000 hours?
A. About 84%
B. About 68%
C. About 32%
D. About 16%
Answer B
disagree. % above +1 SD.
To find the percentage of light bulbs that have a life of more than 3000 hours, we need to calculate the area under the normal distribution curve to the right of 3000.
First, we calculate the z-score using the formula:
z = (x - μ) / σ
where x is the value (3000), μ is the mean (2500), and σ is the standard deviation (500).
z = (3000 - 2500) / 500
z = 500 / 500
z = 1
The z-score of 1 corresponds to the area under the normal distribution curve to the left of the z-score. To find the area to the right, we subtract this value from 1.
Area to the right of z = 1 = 1 - 0.8413
Area to the right of z = 1 ≈ 0.1587
This means that approximately 0.1587, or 15.87%, of light bulbs have a life of more than 3000 hours.
The closest option is D. About 16%.