A Realtor claims that no more than half of the homes he sells are sold for less than the asking price. When reviewing a random sample of 12 sales over the past year, he found that actually 10 were sold below the asking price.

(a) Would we be justified in assuming that the sample proportion p is normally distributed? Explain.

(b) Calculate a p-value for the observed sample outcome, using the normal distribution. At the .05 level of significance in a right-tailed test, is the proportion of homes sold for less than the asking price greater than 50%?

(c) Use Excel to calculate the binomial probability P(X ≥ 10 | n = 12, π = .50) = 1 − P(X ≤ 9 | n = 12, π = .50).