Suppose GRE Quantitative scores are normally distributed with a mean of 587587 and a standard deviation of 152152. A university plans to offer tutoring jobs to students whose scores are in the top 14%14%. What is the minimum score required for the job offer? Round your answer to the nearest whole number, if necessary.

The minimum score required for the job offer is 751.

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.

In this question, we have that:

What is the minimum score required for the job offer?

Top 14%, so the minimum score is the 100-14 = 86th percentile, which is X when Z has a pvalue of 0.86. So X when Z = 1.08.

Then

Rounding to the nearest whole number:

The minimum score required for the job offer is 751.

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step-by-step explanation: