4. The monthly utility bills in a city are normally distributed, with a mean of $115 and a standard deviation of $12. Draw the normal curve, label and shade the area for each question. (25 points) a) If a sample of 36 utility bills are randomly selected, find the probability that the average bill is between $110 and $120. Four decimal places (10 points). b) If a sample of 49 utility bills are randomly selected, find the probability that the average bill is less than $110. Four decimal places (10 points). c) Is the distribution of the sample means in this case normally distributed? Why? (5 points)