A large company produces an equal number of brand-name lightbulbs and generic lightbulbs. The director of quality control sets guidelines that production will be stopped if there is evidence that the proportion of all lightbulbs that are defective is greater than 0.10. The director also believes that the proportion of brand-name lightbulbs that are defective is not equal to the proportion of generic lightbulbs that are defective. Therefore, the director wants to estimate the average of the two proportions. 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 Px represent the proportion of all brand-name lightbulbs that are defective. It is reasonable to assume that X is a binomial random variable. (a) 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? Justify your answer. normal. Is it reasonable to assume that the condition is met? Justify your answer. (b) The standard error of Dx is approximately 0.0156. Show how the value of the standard error is cakulated.