Question

The National Association of Realtors released a survey indicating that a surprising 66% of first-time home buyers purchased their homes with low down payment loans (source: Scholastica Cororaton, “66 Percent of first-time home buyers make a low down payment,” http://economistsoutlook.blogs.realtor.org, Apr. 8, 2015).

a. Suppose 12 out of the 20 first-time home buyers sampled received low down payment loans. Calculate the probability that at least 12 in a sample of 20 first-time buyers would take out a such a loan if the population proportion is 0.66.
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 low down payment loans if the 66% value applies.

Answer 1

Let X is a random variable shows the number of home buyers received low down payment loans. Here X has binomial distrbution with following parameters

n=20 and p=0.66

(a)

The probability that at least 12 in a sample of 20 first-time buyers would take out a such a loan if the population proportion is 0.66 is

(b)

The probability that at least 12 in a sample of 20 first-time buyers would take out a such a loan if the population proportion is 0.53 is

(c)