Managers at an electronics retailer have tracked the frequency with which product rebates are redeemed and found that for their company, 40% of all rebates are actually redeemed. Further, they found the following redemption rates: 50% for a $30 rebate on a

$100 product, 10% for a $10 rebate on a $100 product, and 35% for a $50 rebate on a $200 product.

a. Calculate the weighted average proportion of redemption rates for this retailer using the size of the rebate to establish the weights.

b. A random sample of 20 individuals who purchased an item accompanied by a rebate were asked if they submitted their rebate. Suppose four of the questioned individuals said they did redeem their rebate. If the overall 40% estimate of the redemption rate is correct, determine the expected number of rebates that would be redeemed.