Davey Murphy
09/03/2023 · Senior High School

On a standardized exam, the scores are normally distributed with a mean of 500 and a standard deviation of 40 . Find the z-score of a person who scored 616 on the exam.

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To find the z-score of a person who scored 616 on a standardized exam with a mean of 500 and a standard deviation of 40, you can use the z-score formula: \[ z = \frac{(X - \mu)}{\sigma} \] where: - \(X\) is the score, - \(\mu\) is the mean, - \(\sigma\) is the standard deviation. Plugging in the values: - \(X = 616\) - \(\mu = 500\) - \(\sigma = 40\) Now, substitute these values into the formula: \[ z = \frac{(616 - 500)}{40} \] Calculating the numerator: \[ 616 - 500 = 116 \] Now, divide by the standard deviation: \[ z = \frac{116}{40} = 2.9 \] Thus, the z-score of a person who scored 616 on the exam is **2.9**.

Quick Answer

The z-score is 2.9.
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