Lee Batteries plans to produce a double AA battery, Vitality, which lasts longer than current double AA batteries. From preliminary tests, Vitality batteries have a mean life of 90 hours with a standard deviation of 3 hours under normally distributed data. Lee Batteries decides to produce 100 000 batteries.

a) What is the probability, to four decimal places, that a battery selected at random will last less than 85 hours?

b) How many of the batteries can be expected to last between 87 and 95 hours?