The National Association of Realtors released a survey indicating that a surprising 43% of first-time home buyers purchased their homes with no-money-down loans during 2005. The fear is that house prices will decline and leave homeowners owing more than their homes are worth. PMI Mortgage Insurance estimated that there existed a 50% risk that prices would decline within two years in major metro areas such as San Diego, Boston, Long Island, New York City, Los Angeles, and San Francisco.
a. A survey taken by realtors in the San Francisco area found that 12 out of the 20 first-time home buyers sampled purchased their home with no-money- down loans. Calculate the probability that at least 12 in a sample of 20 first-time buyers would take out no-money-down loans if San Francisco's proportion is the same as the nationwide proportion of no- money-down loans.
b. Determine the probability requested in part a if the nationwide proportion is 0.53.
c. Determine the probability that between 8 and 12 of a sample of 20 first-time home buyers would take out no-money-down loans if the 43% value applies.