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A competency test has scores with a mean of 82 and a standard deviation of 2. A histogram of the data shows that the distribution is normal. Between what two values do about 99.7% of the values lie? SHOW YOUR WORK

(statistics)

Respuesta :

Using the Empirical Rule, it is found that 99.7% of the values lie between 76 and 88.

What is the Empirical Rule?

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, we have that:

  • The mean is of 82.
  • The standard deviation is of 2.

99.7% of the values lie within 3 standard deviations of the mean, hence between:

[tex]82 - 3(2) = 76[/tex]

[tex]82 + 3(2) = 88[/tex]

To learn more about the Empirical Rule, you can take a look at https://brainly.com/question/24537145

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