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Avani earned a score of 50 on Exam A that had a mean of 350 and a standard deviation of 100 . She is about to take Exam B that has a mean of 300 and a standard deviation of 40 . How well must Avani score on Exam B in order to do equivalently well as she did on Exam A? Assume that scores on each exam are normally distributed.
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Step 1 ：Given that Avani scored 50 on Exam A, which had a mean of 350 and a standard deviation of 100.

Step 2 ：We need to find out how well Avani must score on Exam B, which has a mean of 300 and a standard deviation of 40, in order to do equivalently well as she did on Exam A.

Step 3 ：To do this, we first convert Avani's score on Exam A to a z-score using the formula: \(z = (X - μ) / σ\), where \(X\) is the raw score, \(μ\) is the mean, and \(σ\) is the standard deviation.

Step 4 ：Substituting the given values, we get \(z = (50 - 350) / 100 = -3.0\). This means that Avani's score was 3 standard deviations below the mean on Exam A.

Step 5 ：We then convert this z-score to a raw score on Exam B using the formula: \(X = μ + z * σ\), where \(μ\) and \(σ\) are the mean and standard deviation for Exam B, respectively.

Step 6 ：Substituting the given values, we get \(X = 300 + (-3.0) * 40 = 180\).

Step 7 ：So, Avani must score \(\boxed{180}\) on Exam B in order to do equivalently well as she did on Exam A.