A manufacturer claims that the average life of its light bulb is 1,200 hours. Assume that the life of all such bulbs has a normal distribution with mean 1,200 hours, and standard deviation 70 hours. Determine the probability the mean life time of a random sample of 9 bulbs will be:
a) At least 1,180 hours.
b) Between 1,185 and 1,190 hours