Question
A set of data items is normally distributed with a mean of 700 and a standard deviation of 10. Find the data item in this distribution that corresponds to the given \( z \)-score. \( z=-6 \) The data item that corresponds to \( z=-6 \) is \( \square \). (Type an integer or a decimal.)
Ask by Ortiz Stephens. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The data item corresponding to \( z = -6 \) is 640.
Solution
To find the data item corresponding to a z-score of -6, use the formula:
x = μ + zσ
Here, μ = 700 and σ = 10. Plug in the values:
x = 700 + (-6)(10) = 700 - 60 = 640
The data item that corresponds to z = -6 is 640.
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Simplify this solution Beyond the Answer
To find the data item corresponding to a \( z \)-score, you can use the formula: \[ X = \mu + z \cdot \sigma \] Where \( X \) is the data item, \( \mu \) is the mean, \( z \) is the \( z \)-score, and \( \sigma \) is the standard deviation. Plugging in the values: - Mean (\( \mu \)) = 700 - Standard deviation (\( \sigma \)) = 10 - \( z \) = -6 So, \[ X = 700 + (-6) \cdot 10 \] \[ X = 700 - 60 \] \[ X = 640 \] The data item that corresponds to \( z=-6 \) is \( 640 \).
