It has been reported that 25% of the homes in the Minneapolis, Minnesota area have been fully weatherized within the past 10 years. You plan to take a random sample of 100 area homes and will compute the proportion of homes in the sample that have been fully weatherized within the past 10 years. Assume the 25% figure for the Minneapolis area is accurate.
a. Show the distribution of possible sample proportion values here. Describe the shape, center, and standard deviation of this distribution.
b. What % of the sample proportions in this distribution are between .18 and .22?
c. What is the likelihood that the proportion of recently weatherized homes in your sample will be greater than .20?
d. How likely is it that the proportion in your sample will be within 3 standard deviations (that is, + σp) of the proportion of recently weatherized homes in overall Minneapolis area?