The lifetime X of a particular type of light bulb is normally distributed with a mean of 1100 days and a standard deviation of 80 days. The manufacturer randomly selects 400 bulbs of this type and ships them to a tire retailer. a. (3 pts) What is the mean and standard deviation of the sampling distribution of X? b. (7 pts) What is the probability that the average lifetime of these 400 bulbs is between 1097 and 1104 days?