Question

The amount of time a certain brand of light bulb lasts is normally distribued with a mean of 1300 hours and a standard deviation of 90 hours. Using the empirical rule, determine what interval of hours represents the lifespan of the middle 68% of light bulbs.

Answer 1

Answer:

The interval of hours that represents the lifespan of the middle 68% of light bulbs is 1210 hours - 1390 hours.

Step-by-step explanation:

In statistics, the 68–95–99.7 rule, also recognized as the Empirical rule, is a shortcut used to recall that 68%, 95% and 99.7% of the values lie within one, two and three standard deviations of the mean, respectively.

Then,

• P (µ - σ < X < µ + σ) = 0.68
• P (µ - 2σ < X < µ + 2σ) = 0.95
• P (µ - 3σ < X < µ + 3σ) = 0.997

he random variable X can be defined as the  amount of time a certain brand of light bulb lasts.

The random variable X is normally distributed with parameters µ = 1300 hours and σ = 90 hours.

Compute the interval of hours that represents the lifespan of the middle 68% of light bulbs as follows:

$P (\mu - \sigma < X < \mu + \sigma) = 0.68\\\\P(1300-90$

Thus, the interval of hours that represents the lifespan of the middle 68% of light bulbs is 1210 hours - 1390 hours.