\begin{tabular}{l} Use this table or the ALEKS calculator to complete the following. \\ Give your answers to four decimal places (for example, 0.1234). \\ \begin{tabular}{|c|c|}\hline (a) Find the area under the standard normal curve to the right of \( \mathrm{z}=2.25 \). \\ \( \square \)\end{tabular} \\ \hline \( \begin{array}{c}\text { (b) Find the area under the standard normal curve between } \mathrm{z}=0.10 \text { and } \mathrm{z}=1.50 \\ \square\end{array} \) \\ \hline\end{tabular}

To find the area under the standard normal curve using the z-scores, you typically use a z-table or statistical software/calculator. Here's how you can tackle each part: For part (a), to find the area to the right of \( z = 2.25 \), you first find the cumulative area to the left of \( z = 2.25 \) from the z-table. The cumulative area is approximately \( 0.9878 \). Therefore, the area to the right is calculated as: \[ 1 - 0.9878 = 0.0122 \] So, the answer is \( 0.0122 \). For part (b), you will find the cumulative areas for both \( z = 0.10 \) and \( z = 1.50 \). From the z-table: - The cumulative area for \( z = 0.10 \) is approximately \( 0.5398 \). - The cumulative area for \( z = 1.50 \) is approximately \( 0.9332 \). Then, to find the area between \( z = 0.10 \) and \( z = 1.50 \): \[ 0.9332 - 0.5398 = 0.3934 \] So, the answer for part (b) is \( 0.3934 \). Final results: - (a) Area to the right of \( z = 2.25 \): \( 0.0122 \) - (b) Area between \( z = 0.10 \) and \( z = 1.50 \): \( 0.3934 \)