Question

The amount of time a certain brand of light bulb lasts is normally distributed with a

Answer 1

The interval of hours represents the lifespan of the middle 68% of light bulbs, using the empirical rule is, 1210 hours to 1390 hours.

What is empirical rule?

According to the empirical rule, also known as 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95% and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.

$P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) = 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) = 99.7\%$

Here, we had  where mean of distribution of X is \mu  and standard deviation from mean of distribution of X is \sigma

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 50 hours. Thus,

$\mu=1300\\\sigma=90$

Using the empirical rule, the interval of hours represents the lifespan of the middle 68% of light bulbs is,

$P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(1300- 90 < X < 1300+ 90) = 68\%\\P(1210 < X < 1390) = 68\%$

Thus, the interval of hours represents the lifespan of the middle 68% of light bulbs, using the empirical rule is, 1210 hours to 1390 hours.

Learn more about empirical rule here:

brainly.com/question/13676793

#SPJ1