Questions: According to a recent reporting on a standardized test, the average math score for students in a particular state was 555. Assume the scores are Normally distributed with a standard deviation of 100. Answer parts (a) through (c) below including an appropriately labeled and shaded Normal curve for each part. a. What percentage of the math test takers from this state scored 600 or more?

Solution Steps

• Average math score (mean, μ) = 555
• Standard deviation (σ) = 100
• We need to find the percentage of students who scored 600 or more.

The Z-score formula is: \[ Z = \frac{X - \mu}{\sigma} \] Where:

• \( X \) is the score we are interested in (600)
• \( \mu \) is the mean (555)
• \( \sigma \) is the standard deviation (100)

\[ Z = \frac{600 - 555}{100} = \frac{45}{100} = 0.45 \]

Using the Z-score table, we find the area to the left of Z = 0.45. The Z-score table gives us the cumulative probability up to the Z-score.

For \( Z = 0.45 \), the cumulative probability is approximately 0.6736. This means that 67.36% of the students scored below 600.

To find the percentage of students who scored 600 or more, we subtract the cumulative probability from 1.

\[ 1 - 0.6736 = 0.3264 \]

Final Answer