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 100 hours. what percentage light bulbs last more than 1600 hours, to the nearest tenth? statistics calculator

Explanation:

Step1: Recall Normal Distribution Properties

In a normal distribution, the mean ($\mu$) is the center of the symmetric bell - shaped curve. The total area under the normal distribution curve is 1 (or 100% when expressed as a percentage). Since the distribution is symmetric about the mean, the area to the right of the mean ($x > \mu$) is equal to the area to the left of the mean ($x < \mu$), and each of these areas is half of the total area.
Here, the mean $\mu = 1600$ hours. We want to find the percentage of light bulbs that last more than 1600 hours, which is the area to the right of $x = 1600$ in the normal distribution.

Step2: Calculate the Percentage

Since the total area under the normal curve is 1 (100%), and the distribution is symmetric about the mean, the area to the right of the mean is $\frac{1}{2}=0.5$. To convert this to a percentage, we multiply by 100: $0.5\times100 = 50.0\%$ (to the nearest tenth).

Answer:

50.0%