(Solved): (a) What type of variable is "engaged"? The variable is (1) (b) What is the sample proportion of s ...

(a) What type of variable is "engaged"? The variable is (1) (b) What is the sample proportion of students in this high school district who are engaged? $$\hat{p}=$$ (Round to four decimal places as needed.) (c) Verify that the distribution of the sample proportion is approximately normal. The sample size, $$\mathrm{n}=$$ is (2) $$5\%$$ of the population size, or $$0.05\mathrm{N}=$$ (Type integers or decimals. Do not round.) For this sample, $$\widehat{np}(1?\hat{p})=[]$$ (3) 10 . (Round to one decimal place as needed.) $${?}_{\hat{p}}=$$ $${?}_{\hat{p}}=$$ (Round to four decimal places as needed.) $$P(\hat{p}?=$$ (Round to three decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box to complete your choice. (Round to the nearest whole number as needed.) A. If 100 different random samples of 90 students were obtained, at least will have at least 38 students that are engaged. B. If 100 different random samples of 90 students were obtained, would be expected to have at least 38 students that are engaged. C. If 100 different random samples of 90 students were obtained, at most will have at least 38 students that are engaged. D. For every 100 different random samples of 90 students obtained, exactly will have at least 38 students that are engaged. (1) qualitative. (2) less than (3) $$?$$ quantitative and continuous. 1 equal to $$?$$ quantitative and discrete. greater than