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 is less than , 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 when .
Using statistical tables or a calculator, we can find the cumulative probability for a t-distribution with 70 degrees of freedom at .
Let me calculate that for you.The probability that is less than 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:
- How do you calculate probabilities for other values using the t-distribution?
- What is the difference between the t-distribution and the normal distribution?
- How do degrees of freedom affect the shape of the t-distribution?
- How do you find probabilities for positive t-values?
- 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)
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