Answer:
A.
SAT score = 1060
ACT score = 23.2
B.
ACT score = 36.3
Step-by-step explanation:
When the distribution is normal, we use 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.
SAT:
If a student gets an SAT score that is the 62-percentile, find the actual SAT score.
This is X when Z has a pvalue of 0.62. So X when Z = 0.305.
Rounding to the nearest whole number.
SAT score = 1060
ACT:
The equivalent score is X when Z = 0.305.
So
ACT score = 23.2
B. If a student gets an SAT score of 1563, find the equivalent ACT score
Z-score for the SAT score.
Equivalent ACT:
ACT score = 36.3
