Answer to Question #143905 in Statistics and Probability for Vladimyr Lubin

Question

(3.3.9) Consider a value to be significantly low if its z score less than or equal to -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 20.5 and the standard deviation was 4.9. Identify the test scores that are significantly low or significantly high.

What test scores are significantly​ low?
Test scores that are between and

Answer 1

$Sd=4.9$

$2sd=2×4.9=9.8$

Scores that are greater than $20.5+9.8=30.3$ are significantly high.

Scores that are less than $20.5-9.8=10.7$ are significantly low.

Thus, scores between 10.7 and 30.3 are not significantly low or significantly high