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Math  /  Data & Statistics

QuestionA chi-square distribution with 4 degrees of freedom is graphed below. The region under the curve to the right of 9 is shaded.
Find the area of the shaded region. Round your answer to three decimal places. □\square

Studdy Solution

STEP 1

1. The problem involves a chi-square distribution with 4 degrees of freedom.
2. We are asked to find the area to the right of the value 9 under this distribution.
3. The solution requires using a chi-square distribution table or a calculator that can compute chi-square probabilities.

STEP 2

1. Identify the cumulative probability up to the value 9.
2. Subtract the cumulative probability from 1 to find the area of the shaded region.

STEP 3

Use a chi-square distribution table or a calculator to find the cumulative probability P(X≤9) P(X \leq 9) for a chi-square distribution with 4 degrees of freedom.

STEP 4

Using a chi-square distribution calculator or table, find P(X≤9)≈0.899 P(X \leq 9) \approx 0.899 .

STEP 5

Calculate the area of the shaded region to the right of 9 by subtracting the cumulative probability from 1:
P(X>9)=1−P(X≤9) P(X > 9) = 1 - P(X \leq 9)
P(X>9)=1−0.899=0.101 P(X > 9) = 1 - 0.899 = 0.101
The area of the shaded region is approximately:
0.101 \boxed{0.101}

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