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When Boubacar commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 21 minutes and a standard deviation of 4 minutes. Using the empirical rule, what percentage of his commutes will be between 9 and 33 minutes

Sagot :

Using the Empirical Rule, it is found that 99.7% of his commutes will be between 9 and 33 minutes.

What does the Empirical Rule state?

It states that, for a normally distributed random variable:

  • Approximately 68% of the measures are within 1 standard deviation of the mean.
  • Approximately 95% of the measures are within 2 standard deviations of  the mean.
  • Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, considering a mean of 21 minutes and a standard deviation of 4 minutes, we have that:

  • 9 = 21 - 3 x 4.
  • 33 = 21 + 3 x 4.

Within 3 standard deviations of the mean, hence, 99.7% of his commutes will be between 9 and 33 minutes.

More can be learned about the Empirical Rule at https://brainly.com/question/24537145

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