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The exam scores in Bryan's class are Normally
distributed with a mean of 88 points and a standard
deviation of 1.5 points.
Exam Scores
83.5 85 86.5 88 89.5 91 92.5
Score
Which statements are true? Check all that apply.
□ About 16% of all exam scores are less than 86.5
points.
About 16% of all exam scores are greater than 89.5
points.
About 68% of the test scores fall between 85 and 91
points.
About 84% of all exam scores are less than 89.5
points.
About 84% of all exam scores are greater than 89.5
points.
0

Sagot :

Using the Empirical Rule, it is found that the correct statements are given by:

  • About 16% of all exam scores are less than 86.5 points.
  • About 16% of all exam scores are greater than 89.5 points.
  • About 84% of all exam scores are less than 89.5 points.

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.

We also have to consider that the normal distribution is symmetric. Then, alog with the mean of 88 and standard deviation of 1.5, the correct statements are given by:

  • About 16% of all exam scores are less than 86.5 points(more than 1 standard deviation below the mean, the percentage, considering the symmetry, is 0.5 x 32 = 16%).
  • About 16% of all exam scores are greater than 89.5 points, due to the same explanation as above.
  • About 84% of all exam scores are less than 89.5 points, as the percentage is 50%(all below the mean) + 50% x 68%(one standard deviation above the mean) = 84%.

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

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