# For a t-distribution with 15 degrees of freedom, 90% of the distributionis within how many standard deviations of the mean?

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Hello, how do you calculate this? Thank You! help_outlineImage TranscriptioncloseFor a t-distribution with 15 degrees of freedom, 90% of the distribution is within how many standard deviations of the mean? fullscreen
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Step 1

Compute the 90% confidence interval for the population mean.

Since the sample size is small and the population standard deviation is unknown, the 90% confidence interval for the population mean, μ (say) is:

Step 2

Here, degrees of freedom= 15 then n = (15+1) =16 and α = 0.1.

Critical value:

The critical value is obtained using the Excel formula, “=T.INV.2T(0.1, 15)&rdquo...

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