A testing bureau reports that the mean for the population of Graduate Record Exam (GRE) scores is 500 with a standard deviation of 90. The scores are normally distributed. The proportion of scores between 300 and 400 is ___.

The proportion of scores between 300 and 400 is 12.03%.

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:

The proportion of scores between 300 and 400 is

This is the pvalue of Z when X = 400 subtracted by the pvalue of Z when X = 300. So

X = 400

has a pvalue of 0.1335.

X = 300

has a pvalue of 0.0132.

0.1335 - 0.0132 = 0.1203

The proportion of scores between 300 and 400 is 12.03%.

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step-by-step explanation:

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