A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis Ho:μ = 12 against H₁:μ< 12 using a random sample of n = 4 specimens. Calculate the P-value if the observed statistic is = 11.5. Suppose that the distribution of the sample mean is approximately normal. Round your final answer to five decimal places (e.g. 98.76543).

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