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On a standardized exam, the scores are normally distributed with a mean of 300 and a standard deviation of 50. Find the z-score of a person who scored 285 on the exam.

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Final answer:

The z-score of a person who scored 285 on the exam is approximately -0.3, which means the score is 0.3 standard deviations below the mean.

Step-by-step explanation:

To find the z-score of a person who scored 285 on the exam, we can use the formula:

z = (x - μ) / σ

where:

  • z is the z-score
  • x is the individual score
  • μ is the mean of the distribution
  • σ is the standard deviation of the distribution

Plugging in the values, we have:

z = (285 - 300) / 50 = -0.3

Therefore, the z-score of a person who scored 285 is approximately -0.3. This means that the score is 0.3 standard deviations below the mean.

User Adam Liu
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