A t distribution with 6 degrees of freedom is graphed below. The region under the curve to the right of $t_{0.15}$ is shaded. The area of this region is 0.15

Find the value of $t_{0.15}$. Round your answer to three decimal places.
\[
t_{0.15}=\square
\]
\[
\times
\]
\[
5
\]
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Subr

Step 1 ：The problem is asking for the t-value such that the area to the right of it under the t-distribution curve with 6 degrees of freedom is 0.15. This is equivalent to finding the 85th percentile (1 - 0.15 = 0.85) of the t-distribution with 6 degrees of freedom.

Step 2 ：We can use the Percent Point Function (PPF), which is the inverse of the Cumulative Distribution Function (CDF), to find this value. The PPF gives the variable value for a given percentile of a distribution.

Step 3 ：Let's denote the degrees of freedom as \(df = 6\) and the percentile as \(p = 0.85\).

Step 4 ：By using the PPF, we find that the t-value is approximately 1.134.

Step 5 ：So, the value of \(t_{0.15}\) is \(\boxed{1.134}\).