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

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 \(\mu\pm n\sigma\)

• For \(n = 1\): \(\mu-\sigma=69 - 9=60\), \(\mu+\sigma=69 + 9=78\).
• For \(n = 2\): \(\mu - 2\sigma=69-2\times9=69 - 18 = 51\), \(\mu+2\sigma=69+2\times9=69 + 18=87\).
• For \(n = 3\): \(\mu-3\sigma=69-3\times9=69 - 27=42\), \(\mu + 3\sigma=69+3\times9=69+27 = 96\).

Looking at the left - hand side graph:

• The middle value (mean) should be \(69\). But in the left - hand side graph, the middle value is not \(69\).

Looking at the right - hand side graph:

• The values \(42\approx41\) (approximate due to possible graph scaling), \(51\approx50\), \(69\approx68\) (approximate due to possible graph scaling), \(78\approx77\), \(87\approx86\), \(96\approx95\) follow the pattern of a normal distribution with \(\mu = 69\) and \(\sigma = 9\) (allowing for some minor graph - drawing inaccuracies).

Answer:

The graph on the right is the correctly labeled graph of the distribution of final exam scores.