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Daniel earned a score of 18 on Exam A that had a mean of 28 and a standard deviation of 5. He is about to take Exam B that has a mean of 700 and a standard deviation of 40. How well must Daniel 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.

User Logan Lee
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Answer:

600

Explanation:

To determine how well Daniel must score on Exam B in order to do equivalently well as he did on Exam A, we can use the concept of standard scores or z-scores. A z-score indicates how many standard deviations away from the mean a score is.

First, we need to convert Daniel's score on Exam A to a z-score:

z = (18 - 28) / 5 = -2

This tells us that Daniel's score on Exam A is 2 standard deviations below the mean.

We can then use this z-score to find Daniel's equivalent score on Exam B. To do this, we can use the formula:

x = z * σ + μ

Where x is the equivalent score on Exam B, z is the z-score from Exam A, σ is the standard deviation of Exam B, and μ is the mean of Exam B.

x = (-2) * 40 + 700

x = 600

Therefore, Daniel must score 600 on Exam B in order to do equivalently well as he did on Exam A.

Keep in mind that this calculation assumes that the scores on each exam are normally distributed, which may or may not be the case. It also assumes that the two exams are of similar difficulty, which also may not be the case.

User Mercurybullet
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