Question

the amount of time a certain brand of light bulb lasts is normally distributed with a mean of 1400 hours and a standard deviation of 95 hours. using the empirical rule, determine what interval of hours represents the lifespan of the middle 68% of light bulbs. answer attempt 1 out of 3

Explanation:

Step1: Recall empirical rule

For a normal - distribution, about 68% of the data lies within 1 standard deviation of the mean.

Step2: Calculate the lower bound

The lower bound is $\mu-\sigma$, where $\mu = 1400$ (mean) and $\sigma = 95$ (standard deviation). So, $1400 - 95=1305$.

Step3: Calculate the upper bound

The upper bound is $\mu+\sigma$. So, $1400 + 95 = 1495$.

Answer:

The interval is $[1305,1495]$ hours.