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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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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