(30 marks) ABC Dog Food Company located in Ottawa sells large bags of dog food to warehouse clubs. ABC uses an automatic lling process to ll the bags. Weights of the lled bags are approximately normally distributed with a mean of 50 kilograms and a standard deviation of 1.25 kilograms. (a) (5 marks) What is the probability that a lled bag will weigh less than 49.5 kilograms? (b) (5 marks) What is the probability that a randomly sampled lled bag will weigh between 48.5 and 51 kilograms? (c) (10 marks) What is the minimum weight a bag of dog food could be and remain in the top 15% of all bags lled? (d) (10 marks) ABC is unable to adjust the mean of the lling process. However, it is able to adjust the standard deviation of the lling process. What would the standard deviation need to be so that 2% of all lled bags weigh more than 52 kilograms?