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Use the range rule of thumb to identify the values that are significantly​ low, the values that are signficantly​ high, and the values that are neither significantly low nor significantly high.
A test is used to assess readiness for college. In a recent​ year, the mean test score was 19.7 and the standard deviation was 5.3. Identify the test scores that are significantly low or significantly high.
What test scores are significantly​ low? Select the correct answer below and fill in the answer​ box(es) to complete your choice.

Respuesta :

Using the range rule of thumb, it is found that:

  • Scores of 9.1 or lower are significantly low.
  • Scores of 30.3 or higher are significantly high.

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The z-score of a measure X, in a distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

  • It measures how many standard deviations X is from the mean.
  • From the range rule of thumb, if Z <= -2, the measure is significantly low, and if Z >=2, it is significantly high.

  • Mean of 19.7, thus [tex]\mu = 19.7[/tex].
  • Standard deviation of 5.3, thus [tex]\sigma = 5.3[/tex].

Scores that are significantly low:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-2 = \frac{X - 19.7}{5.3}[/tex]

[tex]X - 19.7 = -2(5.3)[/tex]

[tex]X = 9.1[/tex]

Scores of 9.1 or lower are significantly low.

Scores that are significantly high:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]2 = \frac{X - 19.7}{5.3}[/tex]

[tex]X - 19.7 = 2(5.3)[/tex]

[tex]X = 30.3[/tex]

Scores of 30.3 or higher are significantly high.

A similar problem is given at https://brainly.com/question/24126815

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