Use Table 4 as shown in img.jpg to find the following probabilities for a standard normal random variable Z. a. P(0≤Z≤1.2) b. P(-0.9≤Z≤0) c.P(0.3≤Z≤1.56)

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Use Table 4 as shown in img.jpg to find the following probabilities for a standard normal random variable Z.

a. P(0≤Z≤1.2)

b. P(-0.9≤Z≤0)

c.P(0.3≤Z≤1.56)

d. P(-0.2≤Z≤0.2)

e. P(-200≤Z≤-1.56) 

**Table 4: Critical Values of t**

This table provides the critical values of the t-distribution for various degrees of freedom (df) and significance levels (\(\alpha\)). These values are used in statistical hypothesis testing, particularly in t-tests.

**Diagram:**
Above the table is a normal distribution curve with a shaded tail representing the area \(\alpha\) (significance level). The critical value \( t_{\alpha} \) is marked on the horizontal axis, beyond which the area \(\alpha\) lies under the curve.

**Table Columns:**
- **Degrees of Freedom:** Ranges from 1 to 29.
- Critical values are provided for significance levels \(\alpha\) = 0.100, 0.050, 0.025, 0.010, and 0.005.

**Critical Values Chart:**

| Degrees of Freedom | \( t_{0.100} \) | \( t_{0.050} \) | \( t_{0.025} \) | \( t_{0.010} \) | \( t_{0.005} \)  |
|--------------------|----------------|----------------|----------------|----------------|---------------|
| 1                  | 3.078          | 6.314          | 12.706         | 31.821         | 63.657        |
| 2                  | 1.886          | 2.920          | 4.303          | 6.965          | 9.925         |
| 3                  | 1.638          | 2.353          | 3.182          | 4.541          | 5.841         |
| 4                  | 1.533          | 2.132          | 2.776          | 3.747          | 4.604         |
| 5                  | 1.476          | 2.015          | 2.571          | 3.365          | 4.032         |
| 6                  | 1.440          | 1.943          | 2.447          | 3.143          | 3.707         |
| 7                  | 1.415          | 1.895          | 2.365          | 2.998          | 3.499         |
| 8                  | 1.
Transcribed Image Text:**Table 4: Critical Values of t** This table provides the critical values of the t-distribution for various degrees of freedom (df) and significance levels (\(\alpha\)). These values are used in statistical hypothesis testing, particularly in t-tests. **Diagram:** Above the table is a normal distribution curve with a shaded tail representing the area \(\alpha\) (significance level). The critical value \( t_{\alpha} \) is marked on the horizontal axis, beyond which the area \(\alpha\) lies under the curve. **Table Columns:** - **Degrees of Freedom:** Ranges from 1 to 29. - Critical values are provided for significance levels \(\alpha\) = 0.100, 0.050, 0.025, 0.010, and 0.005. **Critical Values Chart:** | Degrees of Freedom | \( t_{0.100} \) | \( t_{0.050} \) | \( t_{0.025} \) | \( t_{0.010} \) | \( t_{0.005} \) | |--------------------|----------------|----------------|----------------|----------------|---------------| | 1 | 3.078 | 6.314 | 12.706 | 31.821 | 63.657 | | 2 | 1.886 | 2.920 | 4.303 | 6.965 | 9.925 | | 3 | 1.638 | 2.353 | 3.182 | 4.541 | 5.841 | | 4 | 1.533 | 2.132 | 2.776 | 3.747 | 4.604 | | 5 | 1.476 | 2.015 | 2.571 | 3.365 | 4.032 | | 6 | 1.440 | 1.943 | 2.447 | 3.143 | 3.707 | | 7 | 1.415 | 1.895 | 2.365 | 2.998 | 3.499 | | 8 | 1.
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