Questions: Scores on a test have a mean of 66 and a standard deviation of 9. Michelle has a score of 57. Convert Michelle's score to a z-score. A. 1 B. -1 C. -9 D. 9

Scores on a test have a mean of 66 and a standard deviation of 9. Michelle has a score of 57. Convert Michelle's score to a z-score. A. 1 B. -1 C. -9 D. 9
Transcript text: Scores on a test have a mean of 66 and a standard deviation of 9 . Michelle has a score of 57 . Convert Michelle's score to a $z$-score. A. 1 B. -1 C. -9 D. 9
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Solution

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Solution Steps

Step 1: Identify the Given Values

We are given the following values:

  • Mean (\(\mu\)) = 66
  • Standard deviation (\(\sigma\)) = 9
  • Michelle's score (\(X\)) = 57
Step 2: Apply the Z-Score Formula

The formula to calculate the z-score is:

\[ z = \frac{X - \mu}{\sigma} \]

Substituting the given values into the formula:

\[ z = \frac{57 - 66}{9} \]

Step 3: Calculate the Z-Score

Perform the calculations:

\[ z = \frac{-9}{9} = -1.0 \]

Final Answer

\(\boxed{-1}\)

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