Let C be the closed, piecewise smooth curve formed by traveling in straight lines between the points (0, 0, 0), (2, 0, 8), (3, 2, 12), (1, 2, 4), and back to the origin, in that order. (Thus the surface S lying interior to C is contained in the plane z = 4x.) Use Stokes' theorem to evaluate the integral ∫C(zcos(x))dx+(x2yz)dy+(yz)dz

People end up tossing 12% of what they buy at the grocery store. assume this is the true population proportion and that you plan to take a sample survey of 540 grocery shoppers to further investigate their behavior. a. calculate the mean and the standard error for the sample proportion p. b. describe the sampling distribution of p in part a. draw a graph of this probability distribution with its mean and standard deviation. what is the probability that your survey will provide a sample proportion more than 15%? c. d. population proportion? what is the probability that your survey will provide a sample proportion within + 0.03 of the