Question

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

Answer 1

Answer:

A. 0.317.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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:

$\mu = 515, \sigma = 109$

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

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{550 - 515}{109}$

$Z = 0.32$

$Z = 0.32$ has a pvalue of 0.6255

X = 460

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{460 - 515}{109}$

$Z = -0.5$

$Z = -0.5$ has a pvalue of 0.3085

0.6255 - 0.3085 = 0.317