Question

The NAR estimates that 23% of all homes purchased in 2004 were considered investment properties. If a sample of 800 homes sold in 2004 is obtained find the probability that at least 175 homes are going to be used as investments.

Answer 1

Answer: 0.7752

Step-by-step explanation:

Given : The proportion of all homes purchased in 2004 were considered investment properties estimated by NAR: p = 0.23

Sample size : n= 800

Required sample proportion : $\dfrac{175}{800}=0.21875$

Now , the probability that at least 175 homes are going to be used as investments will be :

$P(p\geq 0.21875)=P(\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\geq\dfrac{0.21875-0.23}{\sqrt{\dfrac{0.23(1-0.23)}{800}}})\\\\=P(z\geq-0.756)\ \ [\because\ z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}]\\\\=P(z-z)=P(Z$ [using p-value calculator or z-table]

Hence, the required probability = 0.7752