Question

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.

Answer 1

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 $\mu$ and standard deviation $\sigma$, is given by:

$Z = \frac{X - \mu}{\sigma}$

• 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 $\mu = 19.7$.
• Standard deviation of 5.3, thus $\sigma = 5.3$.

Scores that are significantly low:

$Z = \frac{X - \mu}{\sigma}$

$-2 = \frac{X - 19.7}{5.3}$

$X - 19.7 = -2(5.3)$

$X = 9.1$

Scores of 9.1 or lower are significantly low.

Scores that are significantly high:

$Z = \frac{X - \mu}{\sigma}$

$2 = \frac{X - 19.7}{5.3}$

$X - 19.7 = 2(5.3)$

$X = 30.3$

Scores of 30.3 or higher are significantly high.

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