You are planning on junking your old car after it runs an additional 30,000 km. The battery on this car has just failed, and you must decide which of two types of batteries, costing the same amount, to purchase. After some research you have discovered that the lifetime of the first batter is normally distributed with mean life 38,000 km and standard deviation 9,000 km, and the lifetime of the second battery is normally distributed with mean life 34,000 and standard deviation 3,200 km.
If all you care about is that the battery purchased lasts at least 30,000 km, which one should you buy? (Hint: see which one has a greater probability of lasting at least 30,000 km.)
What if you wanted the battery to last for additional 32,000 km instead?