\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 $$ \begin{array}{c} ext { (b) Find the area under the standard normal curve between } \mathrm{z}=0.10 ext { and } \mathrm{z}=1.50 \ \square\end{array} $$ \ \hline\end{tabular}

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\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 $$ \begin{array}{c}	ext { (b) Find the area under the standard normal curve between } \mathrm{z}=0.10 	ext { and } \mathrm{z}=1.50 \ \square\end{array} $$ \ \hline\end{tabular}

UpStudy AI · Accepted Answer

Sure, let's solve each part step by step using the standard normal distribution.

### (a) Area to the right of $$ \mathrm{z} = 2.25 $$

1. **Find $$ \Phi(2.25) $$:** This represents the cumulative probability up to $$ z = 2.25 $$.
   
   Using standard normal tables or a calculator:
   $$
   \Phi(2.25) \approx 0.9878
   $$

2. **Calculate the area to the right:**
   $$
   \text{Area to the right} = 1 - \Phi(2.25) = 1 - 0.9878 = 0.0122
   $$

**Answer:**  
   $$ \boxed{0.0122} $$

---

### (b) Area between $$ \mathrm{z} = 0.10 $$ and $$ \mathrm{z} = 1.50 $$

1. **Find $$ \Phi(1.50) $$ and $$ \Phi(0.10) $$:**
   
   Using standard normal tables or a calculator:
   $$
   \Phi(1.50) \approx 0.9332
   $$
   $$
   \Phi(0.10) \approx 0.5398
   $$

2. **Calculate the area between the two z-scores:**
   $$
   \text{Area} = \Phi(1.50) - \Phi(0.10) = 0.9332 - 0.5398 = 0.3934
   $$

**Answer:**  
   $$ \boxed{0.3934} $$
(a) The area to the right of $$ z = 2.25 $$ is 0.0122. (b) The area between $$ z = 0.10 $$ and $$ z = 1.50 $$ is 0.3934.

Use this table or the ALEKS calculator to complete the following.

Give your answers to four decimal places (for example, 0.1234).

(a) Find the area under the standard normal curve to the right of .

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Use this table or the ALEKS calculator to complete the following. Give your answers to four decimal places (for example, 0.1234). (a) Find the area under the standard normal curve to the right of .