Suppose SAT Writing scores are normally distributed with a mean of 493 and a standard deviation of 108. A university plans to send letters of recognition to students whose scores are in the top 10%. What is the minimum score required for a letter of recognition

The minimum score required for a letter of recognition is 631.24.

Step-by-step explanation:

Problems of normally distributed samples are 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:

What is the minimum score required for a letter of recognition

100 - 10 = 90th percentile, which is the value of X when Z has a pvalue of 0.9. So X when Z = 1.28.

The minimum score required for a letter of recognition is 631.24.

i just took the test, the correct answer is .. 31.5 in.