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A veterinarian finds that weights for the population of each dog breed tend to be approximately normally distributed. The mean weight of beagles is 25 pounds with a standard deviation of 3 pounds. The mean weight for Great Danes is 150 pounds with a standard deviation of 20 pounds. About 68% of beagles weigh between 22 and 28 pounds. Consider these values in terms of the mean and standard deviation only. The interval that would represent a similar percentage of Great Danes would fall between

Sagot :

Using the Empirical Rule, it is found that the interval that would represent a similar percentage of Great Danes would fall between 130 and 170 pounds.

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.

68% fall within 1 standard deviation of the mean, hence for the Great Danes, the values are given as follows:

  • 150 - 20 = 130 pounds.
  • 150 + 20 = 170 pounds.

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

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