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.