Math Problem Statement

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.)

Solution

To find the probability that t70t_{70} is less than 1.579-1.579, 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)t(70) when t=1.579t = -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=1.579t = -1.579.

Let me calculate that for you.The probability that t70t_{70} is less than 1.579-1.579 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.

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Math Problem Analysis

Mathematical Concepts

Statistics
Probability
t-Distribution

Formulas

Cumulative distribution function for the t-distribution
P(t < x) for t-distribution

Theorems

t-Distribution Theorem
Degrees of Freedom

Suitable Grade Level

Undergraduate (Statistics 101)