In: Statistics and Probability
The lifetime of batteries produced are independent with an exponential distribution having a mean of 90 days of continuous use. Consider a random selection of 250 batteries. (a) Find the exact probability that at least 50 of these batteries have a lifetime between 60 and 120 days using a binomial modeling approach. (b) Find the exact probability that at least 50 of these batteries have a lifetime between 60 and 120 days using a Poisson modeling approach. (c) Approximate your answer in part (a) using a normal distribution. (d) Approximate your answer in part (b) using a normal distribution.