Need help with chapter 13 questions . "Sampling distribution models of proportions"

1) It is generally believed that nearsightedness affects about 15% of all children. A local elementary school registered 120 incoming kindergarteners For parts b-d, use the normalcdf command or the invNorm command in your calculator. To receive credit, you must write the command and the values you entered. (8 pts) a) Find the mean and standard deviation of the sampling distribution and describe the sampling distribution using the notation N (p. o) b) What is the probability that less than 10% of the incoming kindergarteners are nearsighted? c) What is the probability that more than 17% of the incoming kindergarteners are nearsighted? d) If this school measures at the 80" percentile for all incoming kindergarten classes, what proportion of incoming kindergarteners are nearsighted? 2) In October of 2019, Gallup asked a random sample of 1,506 Americans which of two approaches to punishing murder they thought was better, the death penalty or life without possibility of parole. For the first time since Gallup began asking the question in 1985, a majority of Americans, 60%, now say life imprisonment is a better approach for punishing murder. 36% favored the death penalty. (9 pts) a) Use the1-PropZInt command in your calculator to find a 95% confidence interval for the proportion of Americans that now believe life imprisonment is a better approach for punishing murder. To receive credit, write the command and the values you entered. b) Interpret your interval above in the context of this problem. c) Use your interval to find the margin of error associated with this confidence interval. d) A local official claims that 65% of Americans believe life imprisonment is a better approach for punishing murder. Does the confidence interval support this claim? Explain. 3) Minnesota Public Radio wants to duplicate a survey conducted in 2016 that found that 65%% of adults living in Minnesota felt that the country was going in the wrong direction. How many people would need to be surveyed for a 90% confidence interval to ensure the margin of error would be 3%? To receive credit, write the formula and the values you entered. Be sure to round properly. (5 pts)