Binomial Distribution Assignment 10. Of the boards that Daniel purchased, what is the expected value for how many he can use? (4 pts 11. What is the standard deviation for usable boards out of the 12 that Daniel purchased? 14 pts 12. What is the probability that Daniel is able to complete the project without purchasing more boards? (Remember, Scenario 1: Learning Tower the project requires 8 usable boards. Would Daniel be able to complete the project if he had more than 8?) (4 pts 13. What is the probability that fewer than 8 of the boards are usable? (4 pts Daniel is building a "learning tower." A learning tower is a small structure that allows small children to help in the 14. After inspecting each board closely at home, he finds that 6 of the boards are defective and need to be replaced, kitchen. The design plans that Daniel is using requires 8 boards of high quality lumber. At the local home improvement leaving him with only 6 usable boards. Would this be considered a significantly low number of usable boards? store, they claim that 82% of the lumber would be high quality, meaning it would be free of defects and usable in this Explain your answer mathematically. (6 pts project. To account for lumber that may be discarded, Daniel purchases 12 boards of lumber from this store. (Assume that Daniel is in a hurry and does not have time to closely inspect the boards while at the store.) Initial Questions 15. If another person were considering this project, and only wanted to make one trip to the home improvement store 1. Show that this situation can be modeled by a binomial distribution. For credit, you must discuss each of the criteria how many boards would you recommend purchasing? Explain your answer mathematically. (4 pts required for a binomial experiment. (12 pts) 2. Define the random variable x in this scenario, using the words of the problem. (2 pts) 3. List all possible values of x for this situation. (2 pts) Scenario 2: Deck 4. On one trial for this scenario, what does "success" mean? Explain using the words of the problem. (4 pts) Eventually, Daniel finishes his project. He feels a lot of pride and accomplishment, so he decides to plan a larger project 5. What is the probability of success in this scenario? (2 pts) - a deck in his back yard. This project will require 80 high quality boards. 6. What is the probability of failure in this scenario? (2 pts) Assume that Daniel is using the same home Improvement store (with an 82% chance that a board will be usable), and Probability Distribution Instructions that he is in too big of a hurry to inspect the lumber closely at the store. In Excel, create a probability distribution for this scenario. Deck Questions Label Column A as "x" and Column B as "P(x)." 16. How many boards should Daniel expect to be usable if he purchases 105 boards? (4 pts) In Column A, list the numbers 0 to 12. In Column B, use BINOM.DIST.RANGE to calculate the probability for each x value. Highlight the probability cells, then right click and select Format Cells. Format the probability cells as "Number" and 17. What is the probability at least 80 will be usable if 105 boards are purchased? (4 pts) have Excel show 4 decimal places. 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 Create a probability histogram using the probabilities you calculated. Format and label it properly. Be sure to use the of the boards are usable? (4 pts "Select Data" button to change the x-axis so it correctly lists the x-values. Probability Distribution Questions 19. Seeing this few usable boards makes Daniel pretty angry. Now he has to waste time returning and replacing boards 7. Copy your finished probability distribution (the table) and paste it below. (12 pts) He calls the home improvement store to complain. He tells the customer service manager, "Your board quality has (Paste your table here.) really gone down. There is no way that 82% of them have are high quality - it's definitely a lower percentage than that." 8. Copy your finished probability distribution histogram (the chart) and paste it below. (12 pts) Is it reasonable for Daniel to claim that the percentage of high quality boards is lower than 82%? Explain your (Paste your histogram here.) answer based on your answer to #18 above, using the idea of significance. (6 pts) 9. What is the shape of your histogram? 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) English (United States) Text Predictions: On Accessibility: Good to go FOCUS Lo
