A survey of 4,581 U.S. households that owned a mobile phone found that 58 percent are satisfied with the coverage of their cellular phone provider. (a) Assuming that this was a random sample construct...

A survey of 4,581 U.S. households that owned a mobile phone found that 58 percent are satisfied with the coverage of their cellular phone provider. (a) Assuming that this was a random sample construct a 90 percent confidence interval for the true proportion of satisfied U.S. mobile phone owners. (b) Why is the confidence interval so narrow? (See The Wall Street Journal, October 23, 2006, p. R4.)