4. The proportion of adult women in the United States is approximately $51 \%$. A marketing survey telephones 400 people at random. a) What is the sampling distribution of the observed proportion that are women? b) What is the standard deviation of that proportion? c) Would you be surprised to find $53 \%$ women in a sample of size 400 ? Explain. d) Would you be surprised to find $48 \%$ women in a sample of size 400 ? Explain. e) Would you be surprised to find that there were fewer than 160 women in the sample? Explain. CS.VS.1317||