In a random sample of 400 carpet shops, it was discovered that 136 of them sold carpets at below the list prices recommended by the manufacturer.

(a) Estimate the percentage of all carpet shops selling below list price.

(b) Calculate an approximate 90% confidence interval for the proportion of shops that sell below list price and explain briefly what this means.

(c) What size sample would have to be taken in order to estimate the percentage to within 2%, with 90% confidence?