Bob is working on two separate probability-related projects. The first involves the variable N, which is the number of consecutively filled bottles of an anticancer drug 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 the battery life L, which 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 N and L for Bob.
(b) Determine P(N = 1, 2, or 3) consecutive units above the weight limit.
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