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7. A pharmaceutical manufacturer is concerned that the impurity concentration in pills should not exceed 3%. It is known that from a particular production run impurity concentrations follow a normal distribution with a standard deviation of 0.4%. A random sample of 64 pills from a production run was checked. Find the probability of the hypothesis test rejecting the null hypothesis at the significance level of 5%, when the true mean impurity concentration is 3.10%. Ho:ul 3% 0.4% Xcrit = X + 20.95 = 3% + 1.645 X = 3.08% V64 P(reject Ho when Ha is true) = Power = P(X > 3.08%|u = 3.1%) 3.08% - 3.1% P Z> 0.4% = P(Z > -0.4) = 65.54% V64