Question

The Welch Adult Intelligence Test Scale is composed of a number of subtests. On one subtest, the raw scores have a mean of 35 and a standard deviation of 6. Assuming these raw scores form a normal distribution, what percent of the data falls between the scores of 23 and 47?

Answer 1

Approximately 95.4% of the data falls between the scores of 23 and 47 on the subtest of the Welch Adult Intelligence Test Scale with a mean of 35 and a standard deviation of 6, based on a normal distribution.

Step-by-step explanation:

The question revolves around finding what percent of the data falls between the scores of 23 and 47 on a subtest of the Welch Adult Intelligence Test Scale, assuming the raw scores are normally distributed with a mean of 35 and a standard deviation of 6. To solve this, we first need to calculate the z-scores for the raw scores of 23 and 47, which can be done using the formula z = (X - μ) / σ, where X is the raw score, μ is the mean, and σ is the standard deviation.

The z-score for a raw score of 23 is:

z = (23 - 35) / 6 = -12 / 6 = -2

The z-score for a raw score of 47 is:

z = (47 - 35) / 6 = 12 / 6 = 2

Using a standard normal distribution table, we can find the area between the z-scores of -2 and 2, which corresponds to the percentage of data within those scores. This area is typically around 95.4%. Hence, approximately 95.4% of the data falls between the scores of 23 and 47 on this test.