Wk 4 Discussion – Central Tendency [due Thurs]Post a total of three (3) substantive responses over at least two (2) separate days for full participation. These posts include your initial discussion, and two (2) replies to your classmates.Word count is not measured; however, ensure there is enough discussion to have a substantive response.Due by Thursday(40 points)Initial Discussion. Respond to each of the following eight (8) questions:Read and understand the selected learning objectives in the Lind et al. (2021) textbook.Chapter 7: LO7-2 Normal Probability, LO7-3 Standard Normal Probability Distribution (calculation)Chapter 8: LO8-1 Sampling Methods, LO8-3 Sampling Distribution of the MeanChapter 9: LO9-1 Point Estimate, LO9-2 Confidence Interval for Population Mean (calculation), LO9-2 Population Standard Deviation, ? UnknownChapter 77A. What are the characteristics of a normal probability distribution?7B. The weekly incomes of shift foremen in the glass industry follow the normal probability distribution with a mean of $3,500 and a standard deviation of $1.000.What is the z value for the income of a foreman who earns $3,000 per week?Chapter 88A. Explain why a researcher would sample a population. For instance, why take 1200 valid samples of registered U.S. voters?8B. Describe four random sampling methods (and the advantages).Chapter 99A. What exactly is a point estimate? For instance, what would be a point estimate of these five flower heights (ft.): 5, 6, 7, 8, 99B. A confidence interval is used in the election polls. On the CBS Evening News, it showed Candidate A at 52% and Candidate B at 45%. The margin of error was 6%. Explain how Candidate B could win.The mean yearly income for construction works in New York has been calculated as $88,000, with a range of $85,000 to $91,000.9C1. If a confidence interval of 95% has been calculated with respect to this data, what does that confidence interval tell us?9C2. What is the effect on the confidence interval gap width as the sample size increases?