Use the ALEKS calculator to solve the following problems. \[ \begin{array}{l}\text { (a) Consider a } t \text { distribution with } 10 \text { degrees of freedom. Compute } P(-1.11

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Sure, let's solve both problems involving the $$ t $$-distribution with the given degrees of freedom (df). We'll use the properties of the $$ t $$-distribution to find the required probabilities and critical values.

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### **Problem (a)**

**Given:**
- Degrees of freedom ($$ df $$) = 10
- We need to compute $$ P(-1.11 < t < 1.11) $$.

**Solution:**

The probability $$ P(-1.11 < t < 1.11) $$ is the area under the $$ t $$-distribution curve between $$ t = -1.11 $$ and $$ t = 1.11 $$. Since the $$ t $$-distribution is symmetric around 0, this can be calculated as:

$$
P(-1.11 < t < 1.11) = 2 \times P(t < 1.11) - 1
$$

To find $$ P(t < 1.11) $$ for $$ df = 10 $$, we can use a $$ t $$-distribution calculator or software.

Using a $$ t $$-distribution calculator:

$$
P(t < 1.11) \approx 0.867
$$

Therefore,

$$
P(-1.11 < t < 1.11) = 2 \times 0.867 - 1 = 0.734
$$

**Answer:**

$$
P(-1.11 < t < 1.11) = 0.734
$$

---

### **Problem (b)**

**Given:**
- Degrees of freedom ($$ df $$) = 16
- We need to find the critical value $$ c $$ such that $$ P(t \geq c) = 0.10 $$.

**Solution:**

To find the value of $$ c $$ such that the area to the right of $$ c $$ under the $$ t $$-distribution curve is 0.10, we look for the 90th percentile ($$ 1 - 0.10 = 0.90 $$) of the $$ t $$-distribution with $$ df = 16 $$.

Using a $$ t $$-distribution table or calculator:

$$
c \approx 1.337
$$

**Answer:**

$$
c = 1.337
$$

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### **Final Answers**

**(a)** $$ P(-1.11 < t < 1.11) = 0.734 $$

**(b)** $$ c = 1.337 $$
$$ P(-1.11 < t < 1.11) = 0.734 $$ $$ c = 1.337 $$

Use the ALEKS calculator to solve the following problems. \[ \begin{array}{l}\text { (a) Consider a } t \text { distribution with } 10 \text { degrees of freedom. Compute } P(-1.11

Ask by Howell Bowers. in the United States

Feb 02,2025

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Use the ALEKS calculator to solve the following problems. \[ \begin{array}{l}\text { (a) Consider a } t \text { distribution with } 10 \text { degrees of freedom. Compute } P(-1.11 Ask by Howell Bowers. in the United States Feb 02,2025