Questions: A set of data items is normally distributed with a mean of 80 and a standard deviation of 5. Convert 80 to a z-score. z80= (Do not round until the final answer. Then round to the nearest hundredth as needed.)

A set of data items is normally distributed with a mean of 80 and a standard deviation of 5. Convert 80 to a z-score. z80= (Do not round until the final answer. Then round to the nearest hundredth as needed.)
Transcript text: A set of data items is normally distributed with a mean of 80 and a standard deviation of 5 . Convert 80 to a z-score. \[ z_{80}= \] $\square$ (Do not round until the final answer. Then round to the nearest hundredth as needed.)
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Solution

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Solution Steps

Step 1: Given Information

We have a normally distributed set of data with the following parameters:

  • Mean (\( \mu \)) = 80
  • Standard Deviation (\( \sigma \)) = 5
Step 2: Z-Score Calculation

To find the z-score for the value \( X = 80 \), we use the formula for the z-score:

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

Substituting the known values:

\[ z = \frac{80 - 80}{5} = \frac{0}{5} = 0.0 \]

Step 3: Result Interpretation

The calculated z-score indicates that the value \( 80 \) is exactly at the mean of the distribution, which corresponds to a z-score of \( 0.0 \).

Final Answer

\(\boxed{z = 0.0}\)

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