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On a standardized exam, the scores are normally distributed with a mean of 250 and a

standard deviation of 20. Find the z-score of a person who scored 310 on the exam.

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Final answer:

In Mathematics, a z-score is calculated using the formula z = (x - μ) / σ. The z-score of a person who scored 310 on an exam with a mean of 250 and standard deviation of 20 is 3, indicating the score is 3 standard deviations above the mean.

Step-by-step explanation:

The subject of the question is Mathematics, specifically dealing with the concept of the standard normal distribution and z-scores. To find the z-score of a person who scored 310 on an exam with a mean of 250 and a standard deviation of 20, we use the z-score formula:

z = (x - μ) / σ

Where x is the raw score, μ (mu) is the mean, and σ (sigma) is the standard deviation. Plugging in the values:
z = (310 - 250) / 20

= 60 / 20

= 3

This means the person's score is 3 standard deviations above the mean. A z-score of 3 indicates that the score is significantly higher than the average score of the distribution, following the empirical rule.

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