a) consider a t distribution with 21 degrees of freedom. Compute P(-1.94<t<1.94). round your answer to at least three decimal places. P(-1.95<t<1.94)=

To compute the probability \( P(-1.94 < t < 1.94) \) for a t-distribution with 21 degrees of freedom, we need to find the cumulative probability at \( t = 1.94 \) and subtract the cumulative probability at \( t = -1.94 \).

The cumulative probability for a t-distribution can be found using a t-distribution table or statistical software. For a t-distribution with 21 degrees of freedom, we'll calculate:

\[
P(-1.94 < t < 1.94) = P(t < 1.94) - P(t < -1.94)
\]

Since the t-distribution is symmetric, we know:

\[
P(t < -1.94) = 1 - P(t < 1.94)
\]

Now, let's compute this probability using appropriate methods for t-distributions.

I'll now calculate this probability for you.The probability \( P(-1.94 < t < 1.94) \) for a t-distribution with 21 degrees of freedom is approximately **0.934**.

Do you want more details or have any questions?

Here are 5 related questions to explore further:
1. What is the significance of degrees of freedom in a t-distribution?
2. How does the t-distribution differ from the normal distribution?
3. What is the probability \( P(t > 1.94) \) for this t-distribution?
4. How does the shape of the t-distribution change with increasing degrees of freedom?
5. What would the probability \( P(-1.94 < t < 1.94) \) be for a normal distribution?

**Tip:** The t-distribution approaches the normal distribution as the degrees of freedom increase.

Consider a t distribution with 21 degrees of freedom. Compute P(-1.94 < t < 1.94). Round your answer to at least three decimal places.

Learn how to compute P(-1.94 < t < 1.94) for a t-distribution with 21 degrees of freedom. This detailed solution covers key statistical concepts, including the properties of the t-distribution and how to use symmetry for probability calculations. The solution is accurate to three decimal places, with a final answer of approximately 0.934.

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