Question
A set of data items is normally distributed with a mean of 70 and a standard deviation of 2 . Convert 67 to a \( z \)-score. \( z_{67}= \) (Type an integer or a decimal.)
Ask by Donnelly Robbins. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( z_{67} = -1.5 \)
Solution
To find the z‑score, use the formula z = (x - μ) / σ.
For x = 67, μ = 70, and σ = 2:
z = (67 - 70) / 2 = -3 / 2 = -1.5
So, z₆₇ = -1.5.
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Simplify this solution Mind Expander
To convert a data item to a \( z \)-score, you can use the formula: \[ z = \frac{(X - \mu)}{\sigma} \] where \( \mu \) is the mean and \( \sigma \) is the standard deviation. Here, \( X = 67 \), \( \mu = 70 \), and \( \sigma = 2 \). So, \[ z_{67} = \frac{(67 - 70)}{2} = \frac{-3}{2} = -1.5 \] Thus, \( z_{67} = -1.5 \).
