Suppose you ran 50 separate simulations. Each of these simulations represent a week (7 days) of working with a molding machine. During each simulation, the average number of the machine's failures per day was recorded. You observed that the mean of all of your sample means follows a normal distribution with a standard deviation of 25 that is, ~N(M, 25). Later you decided to run a hypothesis testing on the population mean with the assumptions below and an alpha = 0.01.

H0 : The population mean is equal to 11

H1 : The population mean is not equal to 11

What would be the lowest and highest values of the sample mean that would allow you to not reject the null hypothesis?