Question

The amount of time a certain brand of light bulb lasts is normally distributed with a mean of 1800 hours and a standard deviation of 25 hours. Using the empirical rule, what percentage of light bulbs last between 1725 hours and 1875 hours?

Answer 1

99.7%

Explanation:

The empirical rule formula states that:

68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ

Step 1

We have to find the number of standard deviations from the mean

μ = Mean = 1800 hours

σ = Standard deviation = 25 hours

For 1725 hours

μ - xσ =

1800 - 25x = 1725

25x = 1800 - 1725

25x = 75

x = 75/25

x = 3

For 1875 hours

1800 + 25x = 1875

25x = 1875 - 180

25x = 75

x = 75/25

x = 3

Step 2

From the above calculation, the bum of standard deviations from the mean is 3

Hence, the percentage of light bulbs last between 1725 hours and 1875 hours is 99.7%