The average lifetime of a certain new cell phone is three years. The manufacturer will replace any cell phone failing within two years of the date of purchase. The lifetime of these cell phones is known to follow an exponential distribution. What is the median lifetime of these phones (in years)? In addition to selecting one of the multiple choice answers, describe what you did step-by-step to arrive at a solution.
a. 0.1941
b. 1.3863
c. 2.0794
d. 5.5452