The lifetime of D sized batteries produced by a local factory is normally distributed with mean 11.5 months and standard deviation 1.5 months.

a)Find the probability that a d sized battery selected at random will have a lifetime of less than 13 months.

b)Find the lifetime of D sized batteries produced that would be at the 67th percentile

c)Nine batteries are selected at random from factory's production line. Find the probability that the mean lifetime of the batteries is between 10.5 and 11.5 months.