Suppose that the drying time for a certain type of paint under specified test conditions is known to be normally distributed with mean 75 minutes and standard deviation 5 minutes. Suppose also that chemists have devised a new additive that they hope will reduce the mean drying time (without changing the standard deviation). A test is then conducted to measure the drying time for a 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.
1. Now suppose that the standard deviation of the drying times to 75 minutes is 2 rather than 5 minutes. Without doing any new calculations, describe how this change would affect your answers to parts a and b. Give an intuitive explanation for your reasoning in both cases.