Question

Anger management scores are normally distributed with a mean of 250 and a standard deviation of 35. On the basis of this distribution determine the following:

The percentage of scores between 250 and 285.

Answer 1

To find the percentage of anger management scores between 250 and 285, calculate the Z-score of 285 and refer to a Z-table. Approximately 84.13% of scores fall between 250 and 285.

Step-by-step explanation:

To solve the mathematical problem involving normally distributed anger management scores with a mean of 250 and a standard deviation of 35, and find the percentage of scores between 250 and 285, we will use the Z-score formula. To do this, we first calculate the Z-score for the score of 285:

Z = (X - μ) / σ
Where:
X = score in question (285)
μ = mean of distribution (250)
σ = standard deviation of distribution (35)

Z = (285 - 250) / 35
Z = 35 / 35
Z = 1

A Z-score of 1 indicates that the score of 285 is 1 standard deviation above the mean. Next, we would consult a standard Z-table to find the percentage of scores falling between the mean and a Z-score of 1. Typically, this is 34.13%. Because the distribution is symmetrical, and 50% of the scores fall above the mean, we add this 34.13% to 50% to find the percentage of scores between the mean of 250 and score of 285.

Percentage = 50% + 34.13%
Percentage = 84.13%

Therefore, approximately 84.13% of the scores fall between 250 and 285.