Suppose GRE Quantitative scores are normally distributed with a mean of 588588 and a standard deviation of 154154. A university plans to send letters of recognition to students whose scores are in the top 12%12%. What is the minimum score required for a letter of recognition? Round your answer to the nearest whole number, if necessary.

The minimum score required for a letter of recognition is 769

Step-by-step explanation:

If GRE Quantitative scores are normally distributed with a mean of 588 and a standard deviation of 154, then, for a value x, the associated z-score is computed as (x-588) / 154. On the other hand, we are looking for a value "a" such that P (X > a) = 0.12 or equivalently P (X < a) = 0.88. But this last expression is equivalent to P ((X-588) / 154 < (a-588) / 154) = 0.88, i. e., (a-588) / 154 is the 88th quantile of the standard normal distribution. Therefore (a-588) / 154 = 1.1750, and so, a = 588 + (154) (1.1750) = 768.95