The sales manager for a hardware wholesaler finds that 305 of the previous 655 calls to hardware store Owners resulted in new product placements. Assume that the 655 calls represent a random sample.

 (a) Find a 90% confidence interval for the long - run proportion of new product placements. 

(b) Interpret the confidence interval developed in (a) 

Problem 4: You are trying to estimate the average amount a family spends on food during a year. In the past, the standard deviation of the amount a family has spent on food during a year has been approximately $1200 (assume $1200 to be the population standard deviation). You will be surveying many families and then noting down their amount spent on food. You will then take the average expenditure across all these families to try and approximate the true (population) average family food expenditure. If you want to be 99% sure that you have estimated the true average family food expenditures within plus/minus $60 of your sample mean, how many families do you need to survey