Answer:
Luis would need to have a SAT score of 574.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean 
and standard deviation 
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Nicole's z-score:
ACT scores have a mean of about 21 with a standard deviation of about 5, which means that 
Nicole gets a score of 24, which means that 
. Her z-score is:
What score would Luis have to have on the SAT to have the same standardized score(z-score) as Nicole's standardized score on the ACT?
Luis would have to get a score with a z-score of 0.6, that is, X when Z = 0.6.
SAT scores have a mean of about 508 with a standard deviation of about 110, which means that 
.
The score is:
Luis would need to have a SAT score of 574.
