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Mathematics, 24.05.2021 14:00 COOLIOMARIS

To estimate the proportion of brand-name lightbulbs that are defective, a simple random sample of 400 brand-name lightbulbs is taken and 44 are found to be defective. Let X represent the number of brand-name lightbulbs that are defective in a sample of 400, and let PXrepresent the proportion of all brand-name lightbulbs that are defective. It is reasonable to assume that X is a binomial random variable. Requried:
One condition for obtaining an interval estimate for Px is that the distribution of Px is approximately normal. Is it reasonable to assume that the condition is met?

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