Answer:
Test scores of 10.2 or lower are significantly low.
Test scores of 31.4 or higher are significantly high.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
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:
Identify the test scores that are significantly low or significantly high.
Significantly low
Z = -2 and lower.
So the significantly low scores are thoses values that are lower or equal than X when Z = -2. So
Test scores of 10.2 or lower are significantly low.
Significantly high
Z = 2 and higher.
So the significantly high scores are thoses values that are higherr or equal than X when Z = 2. So
Test scores of 31.4 or higher are significantly high.