The amount of time a certain brand of light bulb lasts is normally distribued with a mean of 1800 hours and a standard deviation of 35 hours. Using the empirical rule, what percentage of light bulbs last between 1765 hours and 1835 hours?

Question

Giana Middleton

Mathematics

5 January, 07:21

The amount of time a certain brand of light bulb lasts is normally distribued with a mean of 1800 hours and a standard deviation of 35 hours. Using the empirical rule, what percentage of light bulbs last between 1765 hours and 1835 hours?

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Answers (1)

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Marlie Randall · Answer 1

Answer: 68% of light bulbs last between 1765 hours and 1835 hours.

Step-by-step explanation:

The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean. The empirical rule is further illustrated below

68% of data falls within the first standard deviation from the mean.

95% fall within two standard deviations.

99.7% fall within three standard deviations.

From the information given, the mean is 1800 hours and the standard deviation is 35 hours.

1 standard deviation = 1 * 35 = 35

1800 - 35 = 1765 hours

1800 + 35 = 1835 hours

Therefore, 68% of light bulbs last between 1765 hours and 1835 hours.