From a july 2019 survey of 1186 randomly selected americans ages 18-29, it was discovered that 248 of them vaped (used an e-cigarette) in the past week. calculate the sample proportion of americans ages 18-29 who vaped in the past week. round this value to four decimal places. write one sentence each to check the three conditions of the central limit theorem. show your work for the mathematical check needed to show a large sample size was taken. using the sample proportion obtained in (a), construct a 90% confidence interval to estimate the population proportion of americans age 18-29 who vaped in the past week. do this "by hand" using the formula and showing your work ( type your work, no images accepted here). round your confidence limits to four decimal places. verify your result from part (c) using stat ã  proportions stats ã  one sample ã  with summary. inside the box, enter the number of successes, the number of observations, and select confidence interval and click compute! copy and paste your statcrunch result in your document. interpret the statcrunch confidence interval in part (d) in one sentence using the context of the question. use the confidence interval applet (for a proportion) in statcrunch to simulate constructing one thousand 90% confidence intervals assuming the proportion americans ages 18-29 vaping in the past week in the population is p = 0.22 and the sample size n = 1186. once the window is open, click reset and select (or click) 1000 intervals. copy and paste your image into your document. box 1: enter the given population proportion, 0.22box 2: enter the given confidence level 0.90box 3: enter the given sample size, n = 1186compare the "prop. contained" value from part (f) to the confidence level associated with the simulation in one sentence. write a long-run interpretation for your confidence interval method in context in one sentence.