9. A certain type of bacteria occurs in all raw milk. Let X denotes the bacteria count per ml of milk. The public health dep't has found that if the milk is not contaminated, then x- has a normal distribution. The population distribution has a mean of 2250 with standard deviation 300. In a large commercial dairy, the health inspector takes 42 random samples of milk produced each day. At the end of the day the bacteria count in each of the 42 samples is averaged to obtain the sample average bacteria count X . a/ Assuming that the milk is not contaminated , what is the distribution of x ? b/ Assuming that the milk is not contaminated, what is the probability that the sample average bacteria count X for one day is between 2500 and 2600 bacteria/ml