Suppose the proportion of the population in favor of a new law is 0.70. Moreover, consider a distribution of proportions computed from samples of size n = 500.

(a) Verify that the distribution of sample proportions is Normal.

(b) Suppose that you take a sample of size n = 500 and find the sample proportion to be p = 0.80. Approximately how many standard deviations is p from the mean of the distribution of all sample proportions? Round your answer to two decimal places.