66°North, an outdoor apparel store in Iceland, is analyzing the defective items three items—parkas, trousers, and sweaters. From a total of 500 parkas, 780 trousers, and 720 sweaters, it sampled 75, 35, and 43 respectively. The company found that the defective ratio for each product is 0.15 for parkas, 0.2 for trousers, and 0.05 for sweaters.
a. Calculate the population ratio for defective item for the three products.
b. Find the 90% confidence interval for the proportion of the defective items for all three products.