in 2010 FHA mortgages accounted for 33 of all home purchased

in 2010, FHA mortgages accounted for 33% of all home purchased mortgages that were approved. A random sample of 160 mortgages were selected. What is the probability that 56 or more were approved by the FHA?

Solution

The distribution here is Binomial distribution. But since n is large, we approximate it to the normal distribution.

p=0.33.

n=160.

np=mean=52.8

np(1-p)=sd=35.376

x=56

using excel we find

P(x>56)=1-P(x<56)

We use the NORM.DIST function here.

P(x<56)=0.5360

P(X>56)=0.4639.