Binomial Distribution Assignment Probability Distribution Instructions In Excel, create a probability distribution for this scenario. Scenario 2: Deck Eventually, Daniel finishes his project. He feels a lot of pride and accomplishment, so he decides to plan a larger project Scenario 1: Learning Tower Label Column A as "x" and Column B as "P(x)." - a deck in his back yard. This project will require 80 high quality boards Daniel is building a "learning tower. " A learning tower is a small structure that allows small children to help in the In Column A, list the numbers 0 to 12. Assume that Daniel is using the same home improvement store (with an 82% chance that a board will be usable), and kitchen. The design plans that Daniel is using requires 8 boards of high quality lumber, At the local home improvement In Column B, use BINOM.DIST.RANGE to calculate the probability for each x value. that he is in too big of a hurry to inspect the lumber closely at the store. store, they claim that 82% of the lumber would be high quality, meaning it would be free of defects and usable in this Highlight the probability cells, then right click and select Format Cells. Format the probability cells as "Number" and project. To account for lumber that may be discarded, Daniel purchases 12 boards of lumber from this store. (Assume have Excel show 4 decimal places. Deck Questions Create a probability histogram using the probabilities you calculated. Format and label it properly. Be sure to use the 16. How many boards should Daniel expect to be usable if he purchases 105 boards? (4 pts) that Daniel is in a hurry and does not have time to closely inspect the boards while at the store.) "Select Data" button to change the x-axis so it correctly lists the x values. Initial Questions Probability Distribution Questions 1. Show that this situation can be modeled by a binomial distribution. For credit, you must discuss each of the criteria Copy your finished probability distribution (the table) and paste it below. required for a binomial experiment. (12 pts) (12 pts) (Paste your table here.) 17. What is the probability at least BO will be usable if 105 boards are purchased? (4 pts) 8. Copy your finished probability distribution histogram (the chart) and paste it below. (12 pts) (Paste your histogram here.) 9. What is the shape of your histogram? (4 pts) 18. In Daniel's order of 105 boards, he finds that only 75 of them were usable. What is the probability that 75 or fewer 10. Of the boards that Daniel purchased, what is the expected value for how many he can use? (4 pts) of the boards are usable? (4 pts ) 2. Define the random variable x in this scenario, using the words of the problem. (2 pts) 11. What is the standard deviation for usable boards out of the 12 that Daniel purchased? (4 pts) 3. List all possible values of x for this situation. (2 pts) 12. What is the probability that Daniel is able to complete the project without purchasing more boards? (Remember, 19. Seeing this few usable boards makes Daniel pretty angry. Now he has to waste time returning and replacing boards. the project requires 8 usable boards. Would Daniel be able to complete the project if he had more than 8?) (4 pts) 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 82% of them have are high quality - It's definitely a lower percentage than that" 4. On one trial for this scenario, what does "success" mean? Explain using the words of the problem. (4 pts) is it reasonable for Daniel to claim that the percentage of high quality boards is lower than 87%? Explain your answer based on your answer to #18 above, using the idea of significance. (6 pts) 13. What is the probability that fewer than & of the boards are usable? (4 pts) H 5. What is the probability of success in this scenario? (2 pts) 14. After inspecting each board closely at home, he finds that i of the boards are defective and need to be replaced, leaving him with only 6 usable boards. Would this be considered a significantly low number of usable boards? 20. How many boards should Daniel purchase if he wants a 99% chance of finishing the deck without returning to the store? Explain how you got your answer. (4 pts) Explain your answer mathematically (6 pts) 6. What is the probability of failure in this scenario? (2 pts) 15. If another person were considering this project, and only wanted to make one trip to the home improvement store, how many boards would you recommend purchasing? Explain your answer mathernatically. (4 pts) Focus