54. Refer to Example 4.7 Compute the standard error when n=10, 100, 1000 and 10,000. In each case. use the Empirical Rule to predict an interval within which the sample pro- portion is almost certain to fall. Notice that the interval shrinks in width as the sample size increases This is a consequence of the law of large numbers, which states that the sample proportion lends to eventually converge to the population proportion as the sample size increases indefinitely.