Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

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

#SPJ1