Stanford University conducted a study of whether running is healthy for men and women over age 50. Duringthe first eight years of the study, 1.1% of the 695 members of the 50-Plus Fitness Association died. We areinterested 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 population proportion of people over 50 who ran and died in the same eight-year periodO from the sample of 695 members of the 50-Plus Fitness Association. P is the number of peopleover 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. P' is theO estimate of proportion of people over 50 who ran and died in the same eight-year period from thesample of 695 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 from the sampleO of 695 members of the 50-Plus Fitness Association. P' is the population proportion of people over50 who ran and died in the same eight-year period.X is the number of households in the survey where women make the majority of the purchasingO decisions. P' is the population proportion of households where women make the majority of thepurchasing decisions.X is the number of people over 50 who ran and died in the same eight-year period. P' is theO population proportion of people over 50 who ran and died in the same eight-year period from thesample of 695 members of the 50-Plus Fitness Association.b. Which distribution should you use for this problem? Explain your choice.(0.011)(0.989)p'~ N0.011,, since a normal distribution can be used to approximate a695binomial distribution.(0.011)(0.011)695P'- N0.01l,since a normal distribution can be used to approximate abinomial distribution.(0.011)(0.989)695p'- B0.011,since a binomial distribution can be used to approximatea normal distribution,O P'-B(8,0.011), since a binomial distribution can be used to approximate a normal distribution.(0.011)(0.989)695p'- N 8,. since a normal distribution can be used to approximate abinomial distribution. c. Construct a 94% confidence interval for the population proportion of people over 50 who ran and died inthe 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 "94% confidence interval" means for this study.If we took repeated samples of people over 50 who ran over eight years, the sample proportion ofpeople over 50 who ran and died in the same eight-year period would equal the populationproportion in approximately 94% of the samples.If we took repeated samples of people over 50 who ran over eight years, approximately 94% of theconfidence intervals calulated from those samples would contain the true value of the populationproportion 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 94% of theconfidence intervals calulated from those samples would contain the sample proportion of peopleover 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 94% of thesamples would produce the same confidence interval.

Given information: n = 695 P(Died) = 1.1%

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, 1.19% of the 695 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 population proportion of people over 50 who ran and died in the same eight-year period from the sample of 695 members of the 50-Plus Fitness 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. P' is the O estimate of proportion of people over 50 who ran and died in the same eight-year period from the sample of 695 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 from the sample O of 695 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. X is the number of households in the survey where women make the majority of the purchasing O 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. p' is the O population proportion of people over 50 who ran and died in the same eight-year period from the sample of 695 members of the 50-Plus Fitness Association. b. Which distribution should you use for this problem? Explain your choice. p'~ N0.011, (0.011)(0.989) 695 since a normal distribution can be used to approximate a binomial distribution. p'-N0.011, (0.011)(0.011) 695 since a normal distribution can be used to approximate a binomial distribution. (0.011, (0.011)(0.989) p B since a binomial distribution can be used to approximate a normal distribution. o P'- B(8,0.011), since a binomial distribution can be used to approximate a normal distribution. (0.011)(0.989) 695 p' N since a normal distribution can be used to approximate a binomial distribution.