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Nolan earned a score of 380 on Exam A that had a mean of 400 and a standard deviation of 100. He is about to take Exam B
that has a mean of 450 and a standard deviation of 25. How well must Nolan score on Exam B in order to do equivalently
well as he did on Exam A? Assume that scores on each exam are normally distributed.
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Verified Answer :

Answer: 440

Step-by-step explanation:

1. First, we need to calculate Nolan's z-score on Exam A. The z-score is a measure of how many standard deviations an element is from the mean. It is calculated as follows: z = (X - μ) / σ, where X is the score, μ is the mean, and σ is the standard deviation. For Exam A, Nolan's z-score is (380 - 400) / 100 = -0.2.2. To find out how well Nolan must score on Exam B to do equivalently well as he did on Exam A, we need to find the score that corresponds to a z-score of -0.2 on Exam B. We can do this by rearranging the z-score formula to solve for X: X = μ + zσ. For Exam B, the score that corresponds to a z-score of -0.2 is 450 + (-0.2) * 25 = 440.Therefore, Nolan must score 440 on Exam B to do equivalently well as he did on Exam A.

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