In individuals with multiple sclerosis (M5), the immune system attacks the fatty protective myelin sheath that covers the nerve fibers causing communication problems between the brain and the rest ofthe body that can result in permanent damage or deterioration. Approximately 13% of people with MS experience a disease subset known as primaryprogressive (PPMS), characterized by gradual onset and steady progression of signs and symptoms. Dr. Flynn has 19 patients in her practice diagnosed with MS. The number of these with PPMS is recorded. (Note: these patients are known to have MS, but it is unknown whether they have PPlVIS.) lnitlal Questions 1. Let the random variable X be the number of these patients that have PPIVlS. Show that X is a binomial random variable. For credit, you must discuss each of the criteria required for a binomial experiment, in context. (12 pts) 2. What are the possible values ofX for this situation? (4 pts) 3. On one trial for this scenario, what does \"success" mean? Explain using the words ofthe problem. (4 pts) 4. What is the probability of success for one trial in this scenario? (2 pts) 5. What is the probability of failure for one trial in this scenario? (2 pts) Probabiiity Distribution Instructions In Excel, create a probability distribution for this scenario. Label Column A as "X\" and Column B as \"P(X).\" In Column A, list the numbers 0 to 19. 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 have Excel show 4 decimal places. Create a probability histogram using the probabilities you calculated. Format and label it properly. Be sure to use the \"Select Data\" button to change the x-axis so it correctly lists the x-values. Probability Distribution Questions 6. Copy your finished probability distribution (the table) and paste it below. (12 pts) (Paste your table here.) 7. Copy yourfinished probability distribution histogram (the chart) and paste it below. (12 pts) (Paste your histogram here.) 8. 10. 11. 12. l3. 14. What is the shape of your histogram? (4 pts) How many of Dr. Flynn's patients do we expect to have PPMS? (4 pts) What is the standard deviation for the number of PPMS patients from Dr. Flynn's practice? (4 pts) What is the probability that at least 3 patients are found to have PPMS? (4 pts) What is the probability that fewer than 5 have PPM S? (4 pts) What is the probability that between 1 and 5 patients have PPMS (including 1 and 5)? (4 pts) Dr. Flynn is considering referring her PPMS patients to a different practice that specializes in this form of MS. If enough of her patients have PPMS, though, she may bring in a consulting specialist. If 6 of her MS patients are found to have PPMS, would this be considered significantly high, and therefore merit hiring a specialist? Explain your answer mathematically. (6 pts)