Titleabc123 Version X1introduction To Statistical Thinkingqnt351 Ver Complete the following questions, explaining your answers and showing your work: Calculate the probability that any two of 17 people at a party share the same birthday, assuming each day of the year is equally probable and excluding February 29. Show your work. Analyze data from a cold and flu study comparing two medications for sore throats and fever. Determine which medication is better overall based on success rates. Explain your reasoning and discuss the concept of Simpson's Paradox. In a WWII study, a statistician observed more damage to plane fuselages than engines. Explain why he recommended reinforcing the engines despite the higher frequency of fuselage damage, considering the importance of engine damage on flight safety. Use U.S. climate data for your city to create a 60-day spreadsheet of high and low temperatures. Generate histograms for high and low temperatures. Calculate the mean and standard deviation. Determine what percentage of temperatures fall within one and two standard deviations. Compare these percentages to the normal distribution benchmarks, discuss whether the temperatures are normally distributed, and justify your conclusion.
Paper For Above instruction The probability that any two individuals among a group share the same birthday is a classic problem known as the birthday paradox. Although intuition might suggest that with 17 people the likelihood is low, the actual probability is surprisingly high—about 31.5%. This calculation hinges on the complement probability, which considers the chance that no two people share a birthday. Assuming a uniform distribution of birthdays across 365 days (ignoring leap years), the probability that all 17 birthdays are different is calculated by multiplying the probability that each subsequent individual has a birthday different from those already considered. Mathematically, this is expressed as: P(no shared birthday) = (365/365) × (364/365) × (363/365) × ... × (349/365). This can be simplified using permutation notation as P(365,17)/365^17. Therefore, the probability that at least two share a birthday is: P(shared birthday) = 1 - P(no shared birthday) ≈ 1 - 0.685 = 0.315 or 31.5%. This counterintuitive result has many applications in probability and statistics, emphasizing the importance of understanding how probabilities compound in seemingly unlikely scenarios.