Scores on the SAT verbal test in recent years follow approximately the N(515, 109) distribution.

The proportion of students scoring between 460 and 550 is closest to

A. 0.317.

B. 0.309.

C. 0.626.

D. 0.681.

A. 0.317.

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 tha:

The proportion of students scoring between 460 and 550 is closest to

This is the pvalue of Z when X = 550 subtracted by the pvalue of Z when X = 460. So

X = 550

has a pvalue of 0.6255

X = 460

has a pvalue of 0.3085

0.6255 - 0.3085 = 0.317

step-by-step explanation:

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