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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, 2.4% of the 521 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 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 521 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 521 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 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 521 members of the 50-Plus Fitness Association. X is the number of households in the survey where women make the majority of O 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 period O from the sample of 521 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. P' ~ N 0.024, (0.024) (0.976) 621 since a normal distribution can be used to approximate a binomial distribution. O P! ~ N 0.024, 1 (0.024) (0.024) 521 since a normal distribution can be used to approximate a binomial distribution. O P! ~ B 0.024, (0.024) (0.976) 521 since a binomial distribution can be used to approximate a normal distribution. O P' ~B (13, 0.024), since a binomial distribution can be used to approximate a normal distribution. OPI ~ N 13 , 1 (0.024) (0.976) 521 since a normal distribution can be used to approximate a binomial distribution. c. Construct a 99% 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 "99% confidence interval" means for this study, 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 99% of the samples. If we took repeated samples of people over 50 who ran over eight years, approximately 99% 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. O' If we took repeated samples of people over 50 who ran over eight years, approximately 99% 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 99% of the confidence intervals calulated from those samples would contain the true value of the population proportion of people over 50 who ran and died in the same eight-year period