Question

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 high 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 20.8 an 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.

Test scores are not given in this problem.

Answer 1

Solution: We are given that if the z score for any value is less than or equal to -2, then that value is to be considered significantly low.

And if the z score for any value is more than or equal to 2, then that value is to be considered significantly high.

In other words, it means if any value is less than or equal to 2 standard deviation below the mean, then that value will be considered significantly low and if any value is more than or equal to 2 standard deviation above the mean, then that value will be considered significantly high.

We are also given:

Mean test score,

Standard deviation,

Now, let's identify the test scores that are significantly low or significantly high.

The significantly low test score is:

Therefore, the test score less than or equal to 10.2 would be considered significantly low.

The significantly high test score is:

Therefore, the test score greater than or equal to 31.4 would be considered significantly high.