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Svet_ta [14]
3 years ago
15

Consider a value to be significantly low if its z score less than or equal to minus−2 or consider a value to be significantly hi

gh if its z score is greater than or equal to 2. A test is used to assess readiness for college. In a recent​ year, the mean test score was 20.620.6 and the standard deviation was 5.25.2. Identify the test scores that are significantly low or significantly high.
Mathematics
1 answer:
den301095 [7]3 years ago
6 0

Answer:

Test scores of 10.2 or lower are significantly low.

Test scores of 31 or higher are significantly high

Step-by-step explanation:

Z-score:

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 20.6, \sigma = 5.2

Significantly low:

Z-scores of -2 or lower

So scores of X when Z = -2 or lower

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

-2 = \frac{X - 20.6}{5.2}

X - 20.6 = -2*5.2

X = 10.2

Test scores of 10.2 or lower are significantly low.

Significantly high:

Z-scores of 2 or higher

So scores of X when Z = 2 or higher

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

2 = \frac{X - 20.6}{5.2}

X - 20.6 = 2*5.2

X = 31

Test scores of 31 or higher are significantly high

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