Dana is building a "learning tower." A learning tower is a small structure that allows small children to help in the kitchen. The design plans that Dana is using requires 12 boards of high quality lumber. At the local home improvement store, about 89% of the lumber would be high quality, meaning it would be free of defects and usable in this project. To account for lumber that may be discarded, Dana purchases 15 boards of lumber from this store. (Assume that Dana is in a hurry and does not have time to closely inspect the boards while at the store.)

1.In Dana's order of 180 boards, he finds that only 148 of them were usable. What is the probability that 148 or less of the boards are usable?(4 pts)

The probability of

2.Seeing this few usable boards makes Dana pretty angry. Now he has to waste time returning and replacing boards. He calls the home improvement store to complain. He tells the customer service manager, "Your board quality has really gone down. There is no way that 89% of them have are high quality - it's definitely a lower percentage than that."

Is it reasonable for Dana to claim that the percentage of high quality boards is lower than 89%? Explain your answer based on your answer to #18 above, using the idea of significance.(6 pts)

How many boards should Dana purchase if he wants a 99% chance of finishing the deck without returning to the store? Explain how you got your answer.