Questions: Fill in the blank. The represents the number of standard deviations an observation is from the mean.

Fill in the blank. The represents the number of standard deviations an observation is from the mean.
Transcript text: Fill in the blank. The $\square$ represents the number of standard deviations an observation is from the mean.
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Solution

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Solution Steps

Hint

To determine how far an observation is from the mean in terms of standard deviations, use the concept of the z-score or standard score.

Step 1: Identify the Given Values

We are given:

  • Observation (\(X\)) = 75
  • Mean (\(\mu\)) = 70
  • Standard Deviation (\(\sigma\)) = 5
Step 2: Apply the Z-Score Formula

The z-score formula is: \[ z = \frac{X - \mu}{\sigma} \]

Step 3: Substitute the Given Values into the Formula

Substitute \(X = 75\), \(\mu = 70\), and \(\sigma = 5\) into the formula: \[ z = \frac{75 - 70}{5} \]

Step 4: Simplify the Expression

Simplify the numerator: \[ 75 - 70 = 5 \] Then divide by the standard deviation: \[ z = \frac{5}{5} = 1.0 \]

Final Answer

The z-score is: \[ \boxed{1.0} \]

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