PowerPlus, a global battery maker, is studying the lifetimes of its produced alkaline batteries. This step is crucial to understand the quality of the batteries produced. Battery.xlsx contains the lifetimes of 300 sampled batteries (in hours) under study. (a) PowerPlus proposes the exponential distribution as a possible probability distribution to model the distribution of lifetimes of the batteries. What should the optimal parameter be? Draw a Q-Q plot to check if the data follows the proposed exponential distribution (with your suggested parameter).

b) Alex just buys two batteries produced by PowerPlus and labels them as Battery A and Battery B. Alex uses them to power his computer mouse, which requires two batteries to operate. The mouse is extremely sensitive to its power supply, in the sense that if any of the two batteries run out, it can no longer operate. What is the probability that the operating time of Alex's computer mouse with Batteries A and B is less than 3.5 days? Hint: Consider the Binomial distribution with n = 2.

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