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Assume that a set of test scores in an introduction to finance class is normally distributed with a mean of 72 and a standard deviation of 8. use the 68-95-99.7 rule to find the percentage of scores greater than 88.

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gavinkmullen
Percentage of scores greater than 120:::(50-34)%

Using the Empirical Rule, it is found that 2.5% of the scores are greater than 88.

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The Empirical Rule defined that in a normal distribution:

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

In this problem:

  • Mean of 72, standard deviation of 8.
  • 88 = 72 + 2(8), thus, it is 2 standard deviations above the mean.
  • The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.
  • Of the 50% of the measures below the mean, none are above 88.
  • Of the 50% of the measure above the mean, 100 - 95 = 5% are above 88, thus:

[tex]P = 0.05(50) = 2.5[/tex]

2.5% of scores are greater than 88.

A similar problem is given at https://brainly.com/question/24537145

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