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If Jenna scored a 65 on the original test and 80 on the retake, would you consider this an improvement when looking at the class data? If not, what score would she need to show the same improvement as hee classmates? Explain.

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Without knowing the mean and standard deviation of the class, I cannot determine whether Jenna's score of 80 on the retake represents an improvement when looking at the class data.

To show the same improvement as her classmates, Jenna would need to achieve a score that is also one standard deviation above the mean on the retake. This assumes that Jenna's original score is one standard deviation below the mean of the class on the original test.

For example, if the mean of the original test scores was 70 and the standard deviation was 5, and Jenna's original score of 65 was one standard deviation below the mean, then her z-score would be -1. To show the same improvement as her classmates, Jenna would need to achieve a score on the retake that is also one standard deviation above the mean of the retake scores. If the mean of the retake scores was 85 and the standard deviation was also 5, then the score that Jenna would need to achieve would be:

x = μ + z * σ

x = 85 + (1 * 5)

x = 90

Therefore, in this example, Jenna would need to achieve a score of 90 on the retake to show the same improvement as her classmates, assuming that her original score was one standard deviation below the mean.