Math 200 Online Project #1 Due October 21 40 points You may submit the project via email or a hard copy to my office or bring it to the exam. If you submit via email it must be saved in pdf format (see below for how to convert to pdf). Write 'Math 200 Online' on the subject and nothing else. Name your document with your full name starting with your last name and include your full name in the body of the email (not the subject line). I would name my document moss_cindy.pdf and write Cindy Moss in the body of the email. Two point deduction for not doing this. Sorry but I have too many students to rename all the files. All work must be typed (12 point font) using math symbols with the equation editor when appropriate. For example to write a fraction with an exponent use the equation editor so it looks like 2 not (1/2)^3. Word 2007 and above has an equation editor or you can download Daum Equation Editor https://chrome.google.com/webstore/search/equation%20editor other online equation editors are available online. 1 3 If you need a pdf converter, you can download one here. http://www.freepdfconvert.com/ Send the zip file to yourself, open it, rename it in pdf format, and then send it to me. Otherwise the file will not come to me in pdf format and the email subject line will not be correct. Round all answers to 4 decimal places and show all work. The project will be graded on completeness, correctness, and neatness. All work must be shown using methods discussed on the lecture notes. Use correct spelling and grammar in an organized fashion. Space Shuttle When the space shuttle Challenger exploded shortly after lift off, it was the responsibility of the investigation team to find the cause of this tragedy. Their findings assigned the cause of the explosion to the "O-rings" whose function was to contain the rocket fuel within the fuel cells. When the rocket fuel leaked outside the fuel cell, it was ignited by the exhaust and the subsequent explosion followed. The space shuttle had two sets of O-rings. They were assumed to act independently. However, further study proved them to be dependent. Before the next space shuttle was launched, a third set of O-rings was installed. This new O-ring is truly independent of the other two. Watch the video \"Against All Odds Inside Statistics, Random Variables\" There are two statements made in the space shuttle episode that can be proved using statistics. Statement #1 "When the space shuttle was launched, the crew had the same chances of surviving as if they were playing Russian Roulette with a gun having 8 chambers and 1 bullet." (Russian Roulette involves putting one bullet into a gun having 8 bullet chambers, spinning the chambers, putting the gun barrel to your head and pulling the trigger.) Find the following: (Show work) 1. The probability of surviving Russian Roulette 2. The probability of a fatal accident playing Russian Roulette 3. The probability of a field joint functioning. (This is in the video) 4. Assume the six filed joints fastening the O-ring act independently; find the probability the O-Ring functions. 5. Find the probability the O-ring malfunctions. 6. What is your conclusion about statement #1? Be specific. Statement #2 "When the space shuttle was redesigned, it had an additional O-ring installed that was truly independent of the other two O-rings. This new O-ring increased the probability of the O-rings functioning successfully." 7. Using the same 6 field joints and their probabilities, fill in the probability distribution table for the O-rings (the initial set of two O-rings are dependent and act as one O-ring and the newly installed independent O-ring is the second O-ring). Show your work. Event Probability First set of O-rings function and second O-ring functions First set of O-rings malfunction and second O-ring functions First set of O-rings function and second O-ring malfunctions First set of O-rings malfunction and second O-ring malfunctions 8. Use the probabilities from problem 7 to fill in the probability distribution table. x = the number of O-ring malfunctions x 0 1 2 9. P(x) Using the probabilities from problem 8, find: a. the probability of explosion on lift-off b. the probability of a safe lift-off 10. Comment on the effect of having the third O-ring. Be specific on your reasoning using complete sentences. Include justification