Schmidt Welch
07/31/2023 · Elementary School
Question 5 For a population with \( \mu=100 \) and \( \sigma=20 \), what is the \( X \) value corresponding to \( Z=0.50 \) ? 90
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Tutor-Verified Answer
Step-by-step Solution
To find the \( X \) value corresponding to a given \( Z \) score, you can use the formula:
\[
X = \mu + Z \cdot \sigma
\]
Where:
- \( \mu \) is the mean of the population,
- \( Z \) is the Z score,
- \( \sigma \) is the standard deviation of the population.
Given:
- \( \mu = 100 \)
- \( \sigma = 20 \)
- \( Z = 0.50 \)
Now, plug in the values:
\[
X = 100 + 0.50 \cdot 20
\]
Calculating the multiplication:
\[
0.50 \cdot 20 = 10
\]
Now, add this to the mean:
\[
X = 100 + 10 = 110
\]
So, the \( X \) value corresponding to \( Z = 0.50 \) is \( 110 \).
Quick Answer
\( X = 110 \)
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