A manufacturer produces bags of sweets. The weights of the bags are independently distributed with mean 30 grams and standard deviation 5 grams. A random sample of 50 bags of sweets is taken.

(a) (5 points)State the approximately distribution of the mean weight of the bags in the sample, and find the probability that the mean weight of the bags in the sample is less than 28 grams.

(b) (5 points)Suppose another random sample of size n is taken. The probability that the mean weight of bags in this sample is below 28 grams is less than 0.05. Find the minimum required value of n.