The drying time of a certain type of paint under specified test conditions is known to be normally distributed with mean value 75 min and standard deviation 9 min. Chemists have proposed a new additive designed to decrease average drying time. It is believed that drying times with this additive will remain normally distributed with σ = 9. Because of the expense associated with the additive, evidence should strongly suggest an improvement in average drying time before such a conclusion is adopted. Let μ denote the true average drying time when the additive is used. The appropriate hypotheses are H0: μ = 75 versus Ha: μ < 75. Consider the alternative value μ = 74, which in the context of the problem would presumably not be a practically significant departure from H0. (a) For a level 0.01 test, compute β at this alternative for sample sizes n = 144, 841, and 2500. (Round your answers to four decimal places.)