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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Step-by-step Solution
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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