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Stanford University conducted a study of whether running is healthy for men and women over age 50. During the first eight years of the study, 5.5% of the 596 members of the 50-Plus Fitness Association died. We are interested in the proportion of people over 50 who ran and died in the same eight-year period. a. Define the random variables X and P' in words. X is the number of households in the survey where women make the majority of the purchasing decisions. P' is the population proportion of households where women make the majority of the purchasing decisions. X is the number of people over 50 who ran and died in the same eight-year O period. P' is the estimate of proportion of people over 50 who ran and died in the same eight-year period from the sample of 596 members of the 50-Plus Fitness Association. X is the number of people over 50 who ran and died in the same eight-year period. P' is the population proportion of people over 50 who ran and died in the same eight-year period from the sample of 596 members of the 50-Plus Fitness Association. X is the population proportion of people over 50 who ran and died in the same eight-year period from the sample of 596 members of the 50-Plus Fitness O Association. P' is the number of people over 50 who ran and died in the same eight-year period. X is the number of people over 50 who ran and died in the same eight-year period O from the sample of 596 members of the 50-Plus Fitness Association. P' is the population proportion of people over 50 who ran and died in the same eight-year period. b. Which distribution should you use for this problem? Explain your choice. O P ~ N 0.055, (0.055) (0.945) 596 since a normal distribution can be used to approximate a binomial distribution. P' ~ N 0.055, (0.055) (0.055 596 since a normal distribution can be used to approximate a binomial distribution. O P! ~ B 0.055, (0.055) (0.945) 596 since a binomial distribution can be used to approximate a normal distribution. P' ~ B (33, 0.055), since a binomial distribution can be used to approximate a normal distribution. OPI~N 33, 1 (0.055) (0.945) 596 since a normal distribution can be used to approximate a binomial distribution. . Construct a 93% confidence interval for the population proportion of people over 50 who ran and died in the same eight-year period. Enter your answer in interval notation. Round your answer to four decimal places. Do not round any intermediate calculations. d. Explain what a "93% confidence interval" means for this study. If we took repeated samples of people over 50 who ran over eight years, approximately 93% of the confidence intervals calulated from those samples would O contain the true value of the population proportion of people over 50 who ran and died in the same eight-year period. If we took repeated samples of people over 50 who ran over eight years, approximately 93% of the samples would produce the same confidence interval. If we took repeated samples of people over 50 who ran over eight years, O approximately 93% of the confidence intervals calulated from those samples would contain the sample proportion of people over 50 who ran and died in the same eight-year period. If we took repeated samples of people over 50 who ran over eight years, the O sample proportion of people over 50 who ran and died in the same eight-year period would equal the population proportion in approximately 93% of the samples