Questions: Consider a set of data in which the sample mean is 49.6 and the sample standard deviation is 6. Calculate the z-score given that x=48.2. Round your answer to two decimal places.

Consider a set of data in which the sample mean is 49.6 and the sample standard deviation is 6. Calculate the z-score given that x=48.2. Round your answer to two decimal places.
Transcript text: Consider a set of data in which the sample mean is 49.6 and the sample standard deviation is 6. Calculate the $z$-score given that $x=48.2$. Round your answer to two decimal places.
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Solution

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Solution Steps

To calculate the z-score, we use the formula: \( z = \frac{x - \mu}{\sigma} \), where \( x \) is the data point, \( \mu \) is the sample mean, and \( \sigma \) is the sample standard deviation. We will substitute the given values into this formula to find the z-score.

Step 1: Identify the Given Values

We are given the following values:

  • Sample mean (\(\mu\)) = 49.6
  • Sample standard deviation (\(\sigma\)) = 6
  • Data point (\(x\)) = 48.2
Step 2: Apply the Z-Score Formula

The formula for calculating the z-score is: \[ z = \frac{x - \mu}{\sigma} \] Substituting the given values into the formula, we have: \[ z = \frac{48.2 - 49.6}{6} \]

Step 3: Calculate the Z-Score

Perform the calculation: \[ z = \frac{-1.4}{6} = -0.2333 \]

Step 4: Round the Z-Score

Round the z-score to two decimal places: \[ z \approx -0.23 \]

Final Answer

\(\boxed{-0.23}\)

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