Find the probability

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Part 1

Upper P left parenthesis t 70 less than minus 1.579 right parenthesis equalsPt70 < −1.579= 

enter your response here 

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

To find the probability that \( t_{70} \) is less than \( -1.579 \), we can use the **t-distribution**. Since you have a **t-distribution with 70 degrees of freedom**, we need to look up the cumulative probability for \( t(70) \) when \( t = -1.579 \).

Using statistical tables or a calculator, we can find the cumulative probability for a t-distribution with 70 degrees of freedom at \( t = -1.579 \).

Let me calculate that for you.The probability that \( t_{70} \) is less than \( -1.579 \) is approximately **0.0594** (rounded to 4 decimal places).

Would you like further details on this calculation?

Here are 5 related questions for deeper understanding:
1. How do you calculate probabilities for other values using the t-distribution?
2. What is the difference between the t-distribution and the normal distribution?
3. How do degrees of freedom affect the shape of the t-distribution?
4. How do you find probabilities for positive t-values?
5. When should you use the t-distribution instead of the z-distribution?

**Tip:** The t-distribution is useful when working with small sample sizes and unknown population standard deviations.

Find the probability that t70 < -1.579. (Round to 4 decimal places as needed.)

This solution explains how to calculate the probability for a t-distribution with 70 degrees of freedom, finding P(t70 < -1.579). Using statistical tables or a calculator, the result is approximately 0.0594. Learn about the t-distribution, its applications, and related concepts in probability.

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