A contractor built 30 similar homes in a suburban development. The homes have comparable size and amenities, but each has been sold with features that customize the appearance, landscape, and interior. The contractor expects the homes to sell for about $450,000. He expects that one-third of the homes will sell either for less than $400,000 or more than $500,000.
(a) Would a normal model be appropriate to describe the distribution of sale prices?
(b) What data would help you decide if a normal model is appropriate? (You cannot use the prices of these 30 homes; the model is to describe the prices of as-yet-unsold homes.)
(c) What normal model has properties that are consistent with the intuition of the contractor?