A certain type of automobile battery is known to last an average of 1,170 clays with a standard deviation of 150 days. If 900 of these batteries are selected, find the following probabilities for the average length of life of the selected batteries. (Round your answers to four decimal places.) (a) The average is between 1,158 and 1,170. |:| (b) The average is greater than 1,182. |:| (c) The average is less than 930. |:|