: Concerning the sampling distribution of the sample mean: • Generate a population consisting of 6 observations representing students' scores in a certain course. Select a sample of 2 observations. 1. Prove that the mean of the sample mean equals the population mean. 2. Prove that the variance of the sample mean equals the population variance divided by n. 3. Construct a 95% confidence interval for the population mean.

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Areal estate agent is considering changing her cell phone plan. there are three plans to choose from, all of which involve a monthly service charge of $20. plan a has a cost of $.42 a minute for daytime calls and $.17 a minute for evening calls. plan b has a charge of $.52 a minute for daytime calls and $.15 a minute for evening calls. plan c has a flat rate of $80 with 275 minutes of calls allowed per month and a charge of $.38 per minute beyond that, day or evening.a. determine the total charge under each plan for this case: 150 minutes of day calls and 70 minutes of evening calls in a month. (do not round intermediate calculations. round your answer to 2 decimal places. omit the "$" sign in your response.)c. if the agent will use the service for daytime calls, over what range of call minutes will each plan be optimal? (round each answer to the nearest whole number.include the indifference point itself in each answer.)d. suppose that the agent expects both daytime and evening calls. at what point (i.e., percentage of total call minutes used for daytime calls) would she be indifferent between plans a and b?

Royal motor corp. generates a major portion of its revenues by manufacturing luxury sports cars. however, the company also derives an insignificant percent of its annual revenues by selling its sports merchandise that includes apparel, shoes, and other accessories under the same brand name. which of the following terms best describes royal motor corp.? a. aconglomerate b. a subsidiary c. adominant-businessfirm d. a single-business firm