As part of the General Social Survey (GSS) in 2018, a random sample of U.S. adults were asked whether they have ever been told by a health professional that they have depression. In the sample of 1,414 people that received this question, 271 of them said that they have been told that they did have depression. 

a. Suppose in the population of all U.S. adults, 20% have been told by a health professional that they had depression. Also suppose we take random samples of 1,414 adults from the entire population, find the sample proportion that had been told they had depression, and repeat this many times to create a distribution of these sample proportions. What should be the mean and standard deviation of this distribution of sample proportions? 

b. How many standard deviations below the mean of the distribution described in part (a) is the sample proportion from the GSS? 

c. Based on your answer from part (b), and again assuming that 20% of all U.S. adults have been told by a health professional that they have had depression, is it very unlikely that a random sample of 1,414 U.S. adults would only find 271 of them that would say that they have been told they had depression? Explain.