A battery manufacturer guarantees that his batteries will last, on average, 3 years, with a standard deviation of 1 year. His claims are based upon a very large population of his 'good' batteries. A consumer watch group decides to test his guarantee. Their small sample of his 'good' batteries indicates battery lifetimes (in years) of 1.9, 2.4, 3.0, 3.5, and 4.2. Determine the percent confidence that the difference between the watch group's sample variance and manufacture's true variance is due solely to random effects. Next, based upon the manufacturer's battery population average life time and standard deviation, determine the probabilities that a battery lifetime will be less than 1.9 years and between 3 and 4 years.