In the Multilevel Modelling, we analyzed the monetary decision for gym12. Let’s now look at the implications of making yoga stretching mandatory for all new gyms. To do this, you would look at posterior estimates for mu_alpha, mu_beta, sd_alpha, sd_beta - i.e. the parent nodes of the βj and αj nodes. This is a really cool type of modeling as we not only have estimates at the gym level but also estimates at this higher level of the entire Crossfit Gyms enterprise. Think of the higher-level estimates as spawning gyms with the βj and αj drawn as random values from these four parent nodes. Assuming it costs $10 extra for each trial customer to offer yoga stretching and that the value of a customer is $500, what is the probability that this mandatory yoga stretching policy is value-creating for the Crossfit Gyms corporation? Enter your probability as a decimal rounded to the nearest hundredth place (e.g. 0.12,0.52,0.99). 

HINT: you want to simulate a success probability for a new gym. To do this, you should extract the four columns relevant for simulating a new gym: draws %>% select(mu_alpha,mu_beta,sd_alpha,sd_beta) and then follow the generative DAG recipe to get a posterior distribution for the outcomes of interest. Don't get distracted by all the other columns and data frames.