Find the probability

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Part 1

Upper P left parenthesis t 41 greater than minus 0.189 right parenthesis equalsPt41 > −0.189= 

enter your response here 

​(Round to 4 decimal places as​ needed.)

To solve for \( P(t_{41} > -0.189) \), we need to determine the probability that a value from the **t-distribution** with 41 degrees of freedom exceeds \(-0.189\).

This is a **right-tailed t-distribution** problem, so we'll calculate the cumulative probability from the t-table or use statistical software to determine the corresponding probability.

Steps:
1. Since the t-distribution is symmetric around zero, \( P(t_{41} > -0.189) \) can be calculated by looking at \( P(t_{41} < -0.189) \) and subtracting from 1 (for the complement).
2. You would either consult a t-table or use a calculator to determine the cumulative probability for \( t = -0.189 \) and then compute the complement.

Given the value is small and negative, you expect the probability to be slightly above 0.5. Using statistical software:

\[
P(t_{41} > -0.189) \approx 0.5742
\]

Thus, the probability is approximately **0.5742** (rounded to four decimal places).

Would you like further clarification on this? 

Here are 5 related questions to explore:
1. How do you interpret the t-distribution table?
2. What is the significance of degrees of freedom in t-distribution?
3. How would the probability change if \( t_{41} \) was a positive value?
4. What is the relationship between the t-distribution and the normal distribution?
5. How does the probability change with different sample sizes?

**Tip:** Always check the degrees of freedom carefully when using the t-distribution table.

Find the probability Pt41 > -0.189 (Round to 4 decimal places as needed.)

Learn how to calculate the probability Pt41 > -0.189 using the t-distribution with 41 degrees of freedom. This detailed solution explains key statistical concepts, including the complement rule and the symmetry of the t-distribution. Suitable for college-level statistics students.

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