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CCSS Honors 2.3 Example 2

A multiple-choice test has 8 problems. Each problem has 4 answer choices, and only 1 correct answer. You haven’t studied at all, and decide that your only chance to earn at least some points is to guess. Is this situation an example of a binomial distribution? Create a probability distribution for the number of problems you could answer correctly by guessing. What is the probability that your grade on the test will be 80% or greater? Is this an empirical probability or a theoretical probability? Confirm your results using a graphing calculator.
  1. Determine whether this is a binomial distribution.
  2. Make a probability distribution table. Round your results to the nearest ten-thousandth.
  3. Determine the minimum number of problems needed to get an 80% on the test.
  4. Use the distribution table to calculate the probability of guessing 7 or 8 answers correctly. Is this probability empirical or theoretical?
  5. Confirm your probability distribution table using a graphing calculator.