A high school student took two college entrance exams, scoring 1070 on the SAT and 25 on the ACT. Suppose that SAT scores have a
1 answer:
Answer:
His superior z-score indicates better performance on the SAT.
Step-by-step explanation:
In the case of a normal distribution, we utilize the z-score formula.
For a dataset with a mean of and a standard deviation of
, the z-score of a given value X is defined by:
The z-score illustrates how many standard deviations away the given measurement is from the average. Once we calculate the z-score, we refer to the z-score table to locate the p-value corresponding to this z-score. This p-value indicates the likelihood that the measure is less than X, effectively representing the percentile for X. By subtracting the p-value from 1, we derive the probability that the measurement exceeds X.
Identify which exam the student performed better on.
He excelled in the exam where he had a higher z-score.
SAT:
With a score of 1070, thus
SAT averages are 950 with a standard deviation of 155. Therefore, .
ACT:
With a score of 25, thus
ACT averages are 22 with a standard deviation of 4. This implies that
His greater z-score shows that he performed better on the SAT.
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