Module 6 assignment

  

np=100×0.95=95np = 100/ x  0.95 = 95np=100×0.95=95 

nq=100×0.05=5nq = 100 / x 0.05 = 5nq=100×0.05=5 

1. both np≥5np ≥ 5np≥5 and nq≥5nq ≥ 5nq≥5, the sample proportion does have an approximately normal distribution. 

2 . The smallest it could is 100. N ≥ (5/95, 5/0.05) =max 5.263 

C  

rbinom(n, size, prob) is designed for binomial trials. For coin tosses, use rbinom(n, 1, 0.5) to get 0 or 1 outcomes or rbinom(1, n, 0.5) to get the total number of heads. It is vectorized, fast, and statistically correct for Bernoulli or binomial experiments. 

sample(c("H","T"), n, replace=TRUE, prob=c(0.5,0.5)) also works, but it simulates categorical draws, then you count heads yourself. It is more code and less direct for binomial counts. 

Bottom line for probability problems with coin flips: Use rbinom. It maps directly to the binomial model and is simpler for counts or 0 1 draws 

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