Question 4 (8 marks) A certain brand of batteries has a lifetime that has a normal distribution with a mean of 3,750 hours and a standard deviation of 300 hours. a. What proportion of these batteries will last for more than 4,000 hours? b. What proportion of these batteries will last less than 3,600 hours? c. What proportion of these batteries will last between 3,800 and 4,100 hours? d. What lifetime should the manufacturer advertise for these batteries in order that only 2% of the lamps will wear out before the advertised lifetime