LaCrosse Technology is one of many manufacturers of atomic clocks. It makes an atomic digital watch that is radio-controlled and that maintains its accuracy by reading a radio signal from a WWVB radio signal from Colorado. It neither loses nor gains a second in 20 million years. It is powered by a 3-volt lithium battery expected to last three years. Suppose the life of the battery has a standard deviation of 0.3 years and is normally distributed.
a. Determine the probability that the watch's battery will last longer than 3.5 years.
b. Calculate the probability that the watch's battery will last more than 2.75 years.
c. Compute the length-of-life value for which 10% of the watch's batteries last longer.