Casper Computer has diversified into music players, called BUBS, which have a sealed battery that can be replaced only by returning the BUBS to...

Casper Computer has diversified into music players, called BUBS, which have a sealed battery that can be replaced only by returning the BUBS to Casper. Since the price to the customer of such battery replacement is almost as high as buying the next-­‐generation BUBS, battery life has received attention both within Casper and outside. Casper has carried out extensive testing, and has estimated the average battery life to be 2.1 years, with a standard deviation of 0.4 year, and the shape of the histogram of the individual battery lives is well fit by a normal distribution. The battery life follows this pattern regardless of the proportion of time the BUBS is powered on, and regardless of the battery-­‐recharge pattern. (You may use Excel functions to compute the results. If you use Excel, please write up the Excel function(s) to show your work.)

a. Approximately what percent of batteries last for at least 3 years?

b. If Casper offers a battery-­‐replacement warranty of 2 years, approximately what percent of batteries will be subject to replacement under this warranty? (Hint: A battery will be subject to replacement if it fails within the warranty period.)

c. Casper would like to set a warranty period that would expose it to replacing 10% of batteries. What should the warranty period be?