. . (12 points) In a sample of twelve chicken eggs, a laboratory found the mean amount of cholesterol to be 185.0 mg with a standard deviation of 17.6 mg. .:) Find the margin of error for a 90% condence interval for the true population mean amount of cholesterol in -: 11 such eggs. Round to one decimal place. Use the appropriate formula and show your work. -) Construct this 90% confidence interval. Round to one decimal place. Use the appropriate formula and .-how your work. . (12 points) a) We want to conduct a hypothesis test to test the claim that less than 40% of people prefer the -: isle seat on airplanes using a 0.05 signicance level. State the null and alternative hypotheses. ) Suppose the hypothesis test has been conducted and the test statistic is z = 3. Find the P-value. Use ormalcdf and sketch a curve to accompany your answer. Round to three decimal places. C ) State whether you should reject or fail to reject the null hypothesis. Justify your answer. I) State your conclusion in non-technical terms