The president of Colossus.com, Inc., believes that 42% of the firm’s orders come from customers who have purchased from Colossus.com in the past. A random sample of 108,700 orders from the past six months will be used to estimate the proportion of orders placed by repeat customers. 

a. Assume that Colossus.com’s president is correct and the population proportion p = .42. What is the sampling distribution of p̅  for this study? 

b. What is the probability that the sample proportion p̅  will be within .1% of the population proportion? 

c. What is the probability that the sample proportion p̅  will be within .25% of the population proportion? Comment on the difference between this probability and the value computed in part (b). 

d. Suppose the proportion of orders placed by repeat customers for a sample of 108,700 orders from the past six months differs from the population proportion p by more than 1%. How would you interpret this result?