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 studentsProbability 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

# of trials n = 50 studentsProbability 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

What is the probability that at most 40 will do their homework on time?

# of trials n = 50 studentsProbability 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

What is the probability that more than 40 will do their homework on time?

# of trials n = 50 studentsProbability 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

What is the probability that at least 40 will do their homework on time?

On average, how many students do their homework on time?

# of trials n = 50 studentsProbability of a success on any trial = 0.70 (70%)

Average = = np = (50)(0.70) = 35 students