A certain brand of batteries has a lifetime that has a normal distribution with a [mean of 375 days] and a [standard deviation of 30 days.] a) What is the probability of these batteries will last for more than 400 day? b) What is the probability of these batteries will last between 380 and 410 days? c) What lifetime should the manufacturer advertise for these batteries in order that only 0.0217 of the lamps will wear out before the advertised lifetime? d) 25 batteries from this population is selected. What is the probability that their sample mean of these batteries will last for less than 395 days