Question

One year, many college-bound high school seniors in the U.S. took the Scholastic Aptitude Test (SAT). For the verbal portion of this test, the mean was 425 and the standard deviation was 110. Based on this information what percentage of students would be expected to score between 350 and 550

Answer 1

Using the normal distribution, it is found that 62.46% of students would be expected to score between 350 and 550.

Normal Probability Distribution

In a normal distribution with mean $\mu$ and standard deviation $\sigma$, the z-score of a measure X is given by:

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

• It 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, which is the percentile of X.

In this problem, the mean and the standard deviation are respectively, given by: $\mu = 425, \sigma = 110$

The proportion of students that would be expected to score between 350 and 550 is the p-value of Z when X = 550 subtracted by the p-value of Z when X = 350, hence:

X = 550:

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

$Z = \frac{550 - 425}{110}$

$Z = 1.14$

$Z = 1.14$ has a p-value of 0.8729.

X = 350:

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

$Z = \frac{350 - 425}{110}$

$Z = -0.68$

$Z = -0.68$ has a p-value of 0.2483.

0.8729 - 0.2483 = 0.6246

62.46% of students would be expected to score between 350 and 550.

More can be learned about the normal distribution at brainly.com/question/24663213