Binomial Problem Approximately 70% of statistics students do their homework in time for it to be collected and graded. In a statistics class of 50 students, what is the probability that 40 will do their homework on time? # of trials n = 50 students Probability of a success on any trial = 0.70 (70%) Find P(X = 40). Use the pdf (X= tells us this.) binomialpdf(50,0.7,40) = 0.0386

Binomial Problem What is the probability that at most 40 will do their homework on time? # of trials n = 50 students Probability of a success on any trial = 0.70 (70%) Find P(X  40). Use the cdf (X  tells us this.) binomialcdf(50,0.7,40) = 0.9598

Binomial Problem What is the probability that more than 40 will do their homework on time? # of trials n = 50 students Probability of a success on any trial = 0.70 (70%) Find P(X > 40). Use 1 – cdf (X > tells us this) 1 – binomialcdf(50,0.7,40) = 0.0402

Binomial Problem What is the probability that at least 40 will do their homework on time? # of trials n = 50 students Probability of a success on any trial = 0.70 (70%) Find P(X > 40). Use 1 – cdf (X > tells us this but 40 is included and 39 and less are not) 1 – binomialcdf(50,0.7,39) = 0.0789

Binomial Problem On average, how many students do their homework on time? # of trials n = 50 students Probability of a success on any trial = 0.70 (70%) Average =  = np = (50)(0.70) = 35 students