The time until recharge for an experimental car battery of an electric car under moderate use is claimed to follow a normal distribution with a mean of 3 days and a standard and a standard deviation of 6 hours. (a) What proportion of the batteries can last more than 2.5 days before recharge? (b) What is the probability for a randomly selected battery to last between 2 days and 3.5 days before recharge? (c) If a battery has already lasted three days, what is the probability that it can last for another half a day before recharging is required? (d) How long can 98% of the batteries last before recharge? (e) What is the cutoff time for which only 5% of batteries can last? (f) What is the probability that at least 2 out of 5 batteries can last over 3.5 days before recharge