State and describe in detail, the Central Limit Theorem and explain its importance in probability decision analysis. b) After installing a new battery filling technology, Uganda Batteries Ltd claims that the average expected life of its batteries is at least 299 hours. The Uganda National Bureau of Standards, an independent consumer protection agency tested the credibility of this claim by taking a random sample of 200 batteries from the production line which gave an average life of 300 hours with a standard deviation of 8 hours. Requirement: Evaluate Uganda Batteries’ claim by testing at 5% level the Null Hypothesis that the expected life of the new batteries is at least 299 hours.

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