At an intersection, the red-light times are normally distributed with a mean time of 3 minutes and a standard deviation of 0.25 minutes. Using the empirical rule, approximately what percent of red lights last between 2.5 and 3.5 minutes?

Question

Mathematics

Gilbert Ryan

6 November, 21:39

At an intersection, the red-light times are normally distributed with a mean time of 3 minutes and a standard deviation of 0.25 minutes. Using the empirical rule, approximately what percent of red lights last between 2.5 and 3.5 minutes?

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Answers (1)

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Huerta · Answer 1

95%

Step-by-step explanation:

According to the empirical rule,

68% of the distribution falls within 0ne standard deviation of the mean.

95% percent falls within two standard deviations of the mean

99.7% falls within three standard deviations of the mean.

The red-light times are normally distributed with a mean time of 3 minutes and a standard deviation of 0.25

2.5=3-2 (0.25)

3.5=3+2 (0.25)

We can see that 2.5 is two standard deviations below the mean, and 3.5 is two standard deviations above the mean.

Hence the percentage of red lights that lasts between 2.5 and 3.5 is 95%