Problem

Use the ALEKS calculator to solve the following problems.
(a) Consider a t distribution with 5 degrees of freedom. Compute $P(-1.54< t< 1.54)$. Round your answer to at le three decimal places.
\[
P(-1.54< t< 1.54)=
\]

Answer

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Answer

Finally, we round the probability to at least three decimal places to get the final answer. The final answer is \(\boxed{0.816}\).

Steps

Step 1 :The problem is asking for the probability that a random variable following a t-distribution with 5 degrees of freedom falls between -1.54 and 1.54. This is equivalent to finding the cumulative distribution function (CDF) at 1.54 and subtracting the CDF at -1.54.

Step 2 :First, we set the degrees of freedom (df) to 5, and the two x values to -1.54 and 1.54 respectively.

Step 3 :Next, we calculate the CDF at -1.54 and 1.54. The CDF at -1.54 is 0.09209317737810245, and the CDF at 1.54 is 0.9079068226218975.

Step 4 :We then subtract the CDF at -1.54 from the CDF at 1.54 to get the probability. The probability is 0.8158136452437951.

Step 5 :Finally, we round the probability to at least three decimal places to get the final answer. The final answer is \(\boxed{0.816}\).

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