Find the value of $$ t $$ for a $$ t $$-distribution with 32 degrees of freedom such that the area to the right ort equals 0.005 . Round your answer to three decimal places, if necessary.

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We are asked to find the value of $$ t $$ such that
$$
P(T > t) = 0.005,
$$
where $$ T $$ has a $$ t $$-distribution with 32 degrees of freedom. This is equivalent to finding the 99.5th percentile of the $$ t $$-distribution, that is, the value $$ t_{0.995} $$ for 32 degrees of freedom.

The equation can be written in cumulative form as
$$
P(T \leq t) = 0.995.
$$

Most statistical tables or software (such as R or a calculator) can be used to find this quantile. For instance, in R the command would be:
$$
\texttt{qt(0.995, 32)}
$$
which gives approximately $$ t \approx 2.738 $$.

Rounding to three decimal places, the desired value is:
$$
t \approx 2.738.
$$
The value of $$ t $$ is approximately 2.738.

Find the value of \( t \) for a \( t \)-distribution with 32 degrees of freedom such that the area to the right ort equals 0.005 . Round your answer to three decimal places, if necessary.

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