A factory manufacturing light emitting diode LED bulbs claims that their light bulbs lastfor 50,000 hours on the average. To confirm if this is valid, a quality control manager obtained asample of 50 LED light bulbs and got a mean lifespan of 40,000 hours. The standard deviation ofthe manufacturing process is 1000 hours.1. What is the best point estimate for the true mean life span of the LED light bulbsmanufactured by this factory.2. What is the standard error of this point estimate?3. What is the margin of error of this point estimate?4. Construct a 95% confidence interval of the true mean life span of LED light bulbsmanufactured by this factory.5. Do you think that the claim of the manufacturer is valid? Explain.6. If you want to be 99% confident that the point estimate is at most 100 hours from the truemean life span, how many light bulbs should be included in the sample?

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