Assume that the drying time for certain kind of paint under specified test situations is known to be normally distributed with mean 75 minutes as well as standard deviation 5 minutes. Assume also which chemists have devised the new additive that they hope will reduce the mean drying time (without changing the standard deviation). A test is then conducted to evaluate the drying time for test specimen, and the company executives decide that they will be convinced that the additive is effective only if the drying time on this specimen is less than
70 minutes.
a. If the additive actually has no effect at all on the drying time, what is the probability the company executives will mistakenly conclude that it is effective? Include a sketch with your calculation.
b. If you want to alter the cutoff value from 70 in order to reduce the error probability in part a to .05, what cutoff value should you choose?