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10. A manufacturer of automobile batteries claims that the distribution of the lengths of life of its best batteries has a mean of 60 months and a standard deviation of 7 months. Suppose a consumer group decides to check the claim by purchasing a sample of 50 of these batteries and subjecting them to tests that determine their lives. (i) Assuming that the manufacturer's claim is true, describe the sampling distribution of the mean lifetime of a sample of 50 batteries. (ii) Assuming that the manufacturer's claim is true, what is the probability that the consumer group's sample has a mean life of 57.5 or fewer months