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Statistics Homework Probability Problems Solved

Learn to calculate probabilities of students doing homework on time using binomial distribution. Solve problems step by step. Understand how to find average number of students.

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Statistics Homework Probability Problems Solved

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  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

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