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100 students take a test. The mean score of the results is 88% with a standard deviation of 4%. Considering that the results were normally distributed, what is the median of the graph, what scores are within 2 standard deviations away, and how many student's scores would be within 1 standard deviation from the mean?

Sagot :

Using the Empirical Rule, it is found that:

  • Scores between 80% and 96% are within 2 standard deviations of the mean.
  • 68 scores are within one standard deviation of the mean.

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.

Considering the mean of 88% and the standard deviation of 4%, the scores that are within 2 standard deviations of the mean are:

  • 88 - 2 x 4 = 80%.
  • 88 + 2 x 4 = 96%.

68% are within 1 standard deviation of the mean, hence, out of 100:

0.68 x 100% = 68 scores.

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

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