Lucky Pizzas, where your food is presented with a smile and a poem, delivers its wide assortment of pizzas in an average time of 24 minutes with a standard deviation of 6 minutes. The delivery times are approximately normally distributed.

1. The owner of Lucky Pizzas has promised that any household waiting more than 33 minutes to receive its order will get the pizza(s) free. What is the probability of receiving a free pizza?

2. If 200 orders were received in one night, how many would you expect to take between 15 and 33 minutes to be delivered? Show all workings.

3. On a night in which 100 deliveries were made, the average waiting time was 25 minutes. Calculate the probability the average delivery time exceeds 25 minutes.

4. Does your answer to (3) indicate that the average delivery time is now significantly greater than 24 minutes? Briefly explain (use α=0.05). Note: In effect, you are testing H0: µ ≤ 24 v H1: µ >24.