Bob is working on two separate probability-related projects. The first involves a variable N, which is the number of consecutively manufactured parts that weigh in above the weight specification limit. The variable N is described by the formula (0.5) N because each unit has a 50-50 chance of being below or above the limit. The second involves a battery life L that varies between 2 and 5 months. The probability distribution is triangular with the mode at 5 months, which is the design life. Some batteries fail early, but 2 months is the smallest life experienced thus far.

(a) Write out and plot the probability distributions and cumulative distributions for Bob.

(b) Determine the probability of N being 1, 2, or 3 consecutive units above the weight limit.