The proportion of homes in Mississippi owned by investors rather than homeowners is 25%. Consider a sampling distribution where n=120

(a) A news headline claims that more than a third of all homes sold are being sold to investors rather than homeowners. Determine the P(X>0.33) for Mississippi to determine if the claim is reasonable.

P(X>0.33)=

Is the claim reasonable?

• The claim is unreasonable. If 25% of homes are being sold to investors, there is less than a 5% chance that a sample of homes sold had more than 33% sold to investors by chance alone
• The claim is reasonable. If 0.25 of homes are being sold to investors, there is more than a 5% chance that a sample of homes sold had more than 33% sold to investors by chance alone

(b) What is the probability that between 21% and 29% of homes sold in Mississippi are sold to investors?

P(0.21