The amount of time a certain brand of light bulb lasts is normally distribued with a mean of 1400 hours and a standard deviation of 55 hours. Using the empirical rule, what percentage of light bulbs last between 1345 hours and 1455 hours?

Question

Mathematics

Thalia Fischer

3 March, 14:19

The amount of time a certain brand of light bulb lasts is normally distribued with a mean of 1400 hours and a standard deviation of 55 hours. Using the empirical rule, what percentage of light bulbs last between 1345 hours and 1455 hours?

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Answers (1)

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Kara · Answer 1

By the Empirical Rule, 68% of light bulbs last between 1345 hours and 1455 hours

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 1400 hours

Standard deviation = 55 hours

Using the empirical rule, what percentage of light bulbs last between 1345 hours and 1455 hours?

1345 = 1400 - 1*55

So 1345 is one standard deviation below the mean.

1455 = 1400 + 1*55

So 1455 is one standard deviation above the mean.

By the Empirical Rule, 68% of light bulbs last between 1345 hours and 1455 hours