Question

historically, scores on the mathematical ideas final exam have been normally distributed with mean 69 points and standard deviation 9 points.
choose the correctly labeled graph of the distribution of final exam scores.
distribution of scores
distribution of scores
distribution of scores

Explanation:

Step1: Recall normal distribution properties

In a normal distribution, the mean is at the center. Given mean \(\mu = 69\) and standard deviation \(\sigma=9\).

Step2: Calculate values at \(\mu\pm\sigma\), \(\mu\pm2\sigma\), \(\mu\pm3\sigma\)

• \(\mu-\sigma=69 - 9=60\)
• \(\mu+\sigma=69 + 9=78\)
• \(\mu - 2\sigma=69-2\times9=69 - 18 = 51\)
• \(\mu+2\sigma=69 + 2\times9=69+18 = 87\)
• \(\mu-3\sigma=69-3\times9=69 - 27=42\)
• \(\mu+3\sigma=69+3\times9=69 + 27=96\)

Looking at the second distribution (middle one):

• The middle value (mean) is \(69\)
• Values: \(69 - 2\times9=51\) (approx \(53\) if there is some rounding in graph - scale interpretation), \(69+2\times9 = 87\) (approx \(85\) if scale - rounding), \(69-9 = 60\) (approx \(61\) if scale - rounding), \(69 + 9=78\) (approx \(77\) if scale - rounding)

Answer:

The second (middle) distribution labeled "Distribution of Scores" is the correct one.