(Solved): help with the problems. Show your work. 20 points total. Each numbered problem is worth 4 points. 1 ...

help with the problems. Show your work. 20 points total. Each numbered problem is worth 4 points. 1) Imagine you work for an airline and want to determine the proportion of flights that are more than 10 minutes late. You take a simple random sample of 177 flights and find that 12 of the flights are more than 10 minutes late. Use a 92% confidence level to estimate the proportion of late flights. a) Sketch the distribution curve showing the area in the tails and the critical values. What are the critical values? b) What is the margin of error? (Show the expression that gives the margin of error with the numbers in place and calculate the value. d) c) Write the confidence interval as a compound inequality. (For example: 0.58 < p <0.64) How big should the sample size be if you want the margin of error to be 2% using the same confidence level? (Assume you do not know the sample proportion.)