The height of the water level in mineral water bottles has a mean of 140 mm and a standard deviation of 4 mm. Assume that the height of the water level is normally distributed and water levels in different bottles are independent.
(a) Determine the probability that the average height of the water level of 9 bottles is between 138 mm and 142 mm.
(b)Determine the minimum number of bottles that need to be measured such that the probability that the average height exceeds 142 mm is less than or equal to 0.1