The lifetime of a certain type of automatic washing machine is normally distributed with mean and standard deviation equal to 3.1 and 1.1 years respectively.
(a) If this type of washing machine is guaranteed for one year, what percentage of original sales will require replacement if they fail within the guarantee period?
(b) What percentage of these washing machines is likely to be operating after 4 years? After 5.5 years?
(c) If the manufacturer of these washing machines wants to ensure that no more than 5% of these washers will be replaced within a guarantee period, what new guarantee period should they choose?
Note: Calculate the results for (a)-(c) using the z-table and then the appropriate Excel function (i.e. NORMDIST or NORMINV).