Assume that the mean life of a particular brand of car battery is normally distributed with a mean of 28 months and a standard deviation of 4 months.
(a) For a randomly selected battery, what is the probability that it will last between 30 and 34 months?
(b) What is the probability that a randomly selected battery will fail within two years of the date of purchase?
(c) By what time period will 60% of all batteries of this make fail?
(d) If a guarantee period is to be set, how many months would it have to be to replace no more than 5% of batteries of this make?
Note: Calculate the results for (a) and (b) using the z-table and then the appropriate Excel function (i.e. NORMDIST or NORMINV).