The service life of a hearing aid battery has a normal distribution with a mean of 60 months ...

  

The service life of a hearing aid battery has a normal distribution with a mean of 60 months and a standard deviation of 10 months.

(a) What is the probability that a randomly selected battery will last longer than 53 months?

(b) If 7 batteries are selected at random, what is the probability that at least 3 of them will last longer than 53 months each?

(c) If 16 batteries are selected at random, what is the probability that average life of these 16 batteries will exceed 53 months?

(d) Any battery that stops working during the warranty period will be replaced free of charge by the manufacturer. By manufacturer’s policy, the warranty period is always given in whole number of months (integer values only). What should the warranty period be if the manufacturer does not want to replace more than 1.7% of all the batteries sold?