A certain strain of bacreria occurs in all raw milk. Let x be the bacteria count per millitier of milk. The health department has found that if the milk is not contaminated, then x has an approximately normal distribution. The mean of the distribution is 2500 and the standard deviation is 300. When raw milk has bacteria count greater than 3000 per ml it is considered unsafe for human consumption and must be discarded.

Suppose the dairy worker uses an average x for two samples taken three hours apart.

a) What can be said about the probability distribution of x?

b) What is the probability of x being greater than 3000?

c) The dairy worker decides to increase the number of samples taken (just to be sure) to 3 samples three hours apart. What is the probability of x being greater than 3000 for those three samples?