Luke’s teacher has assigned each student in his class an online quiz, which is made up of 10 multiple-choice questions with 4 options each. Luke hasn’t been paying attention in class and has to guess on each question. However, his teacher allows each student to take the quiz three times and will record the highest of the three scores. A passing score is 6 or more correct out of 10. We want to perform a simulation to estimate the score that Luke will earn on the quiz if he guesses at random on all the questions.

a. Describe how to use a random number generator to perform one trial of the simulation. The dotplot shows Luke’s simulated quiz score in 50 trials of the simulation.

b. Explain what the dot at 1 represents.

c. Use the results of the simulation to estimate the probability that Luke passes the quiz.

d. Doug is in the same class and claims to understand some of the material. If he scored 8 points on the quiz, is there convincing evidence that he understands some of the material? Explain your answer.

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1 2 3 5 Simulated quiz score