Question

The amount of time a certain brand of light bulb lasts is normally distributedwith a mean of 1200 hours and a standard deviation of 100 hours. Using theempirical rule, what percentage of light bulbs last between 1100 hours and1300 hours?

Answer 1

Approximately 68% of the light bulbs last between 1100 hours and 1300 hours.

Step-by-step explanation:

To find the percentage of light bulbs that last between 1100 hours and 1300 hours, we can use the empirical rule, also known as the 68-95-99.7 rule. According to this rule, for a normally distributed data set, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations of the mean, and 99.7% falls within three standard deviations of the mean.

In this case, the mean is 1200 hours and the standard deviation is 100 hours. To find the percentage of light bulbs that last between 1100 hours and 1300 hours, we need to calculate how many standard deviations away these values are from the mean.

First, we calculate the z-score for 1100 hours using the formula: z = (x - mean) / standard deviation. So, z = (1100 - 1200) / 100 = -1. The z-score for 1300 hours is z = (1300 - 1200) / 100 = 1.

The percentage of light bulbs that last between 1100 hours and 1300 hours is the percentage of data that falls within one standard deviation of the mean. Since the empirical rule tells us that approximately 68% of the data falls within one standard deviation of the mean, the percentage of light bulbs that last between 1100 hours and 1300 hours is also approximately 68%.