**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.