The phenomenon of bottle flipping has hit the nation. You design a machine that can randomly flip a bottle. You observe 2080 random, independent flips, and 368 land the correct way. Estimate the overall proportion of bottles that land correctly when flipped randomly. Use a 99% confidence level. Round everything to 3 decimal places.
a) State the parameter of interest. Verify that the necessary conditions are present in order to carry out the procedure.

b) Find the critical value and standard error.
Critical Value: Standard Error:
c) Find the confidence interval: (,)
d) Interpret the 99% confidence interval in context.