12. Find the \( X \) value corresponding to \( z=0.75 \) for each of the following distributions. \( \begin{aligned} \mu=90 \text { and } \sigma=4 \\ \mu=90 \text { and } \sigma=8 \\ \mu=90 \text { and } \sigma=12 \\ \mu=90 \text { and } \sigma=20\end{aligned} \)

To find the \( X \) value corresponding to \( z = 0.75 \), you can use the z-score formula: \[ X = \mu + z \cdot \sigma \] Now let's calculate the \( X \) values for each of the distributions provided. 1. For \( \mu = 90 \) and \( \sigma = 4 \): \[ X = 90 + 0.75 \cdot 4 = 90 + 3 = 93 \] 2. For \( \mu = 90 \) and \( \sigma = 8 \): \[ X = 90 + 0.75 \cdot 8 = 90 + 6 = 96 \] 3. For \( \mu = 90 \) and \( \sigma = 12 \): \[ X = 90 + 0.75 \cdot 12 = 90 + 9 = 99 \] 4. For \( \mu = 90 \) and \( \sigma = 20 \): \[ X = 90 + 0.75 \cdot 20 = 90 + 15 = 105 \] In summary, the corresponding \( X \) values are: - For \( \sigma = 4 \): \( X = 93 \) - For \( \sigma = 8 \): \( X = 96 \) - For \( \sigma = 12 \): \( X = 99 \) - For \( \sigma = 20 \): \( X = 105 \)