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.
Describe how to use a random number generator to perform one trial of the simulation.
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The dotplot shows Luke’s simulated quiz score in 50 trials of the simulation.
Explain what the dot at 1 represents.
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Use the results of the simulation to estimate the probability that Luke passes the quiz.
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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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The Transportation Security Administration (TSA) is responsible for airport safety. On some flights, TSA officers randomly select passengers for an extra security check prior to boarding. One such flight had 76 passengers—12 in first class and 64 in coach class. Some passengers were surprised when none of the 10 passengers chosen for screening were seated in first class. We want to perform a simulation to estimate the probability that no first-class passengers would be chosen in a truly random selection.
Describe in excrutiating detail how you would use a table of random digits to carry out this simulation.
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Perform one trial of the simulation using the random digits that follow.
How many of the 10 passengers selected were first class? Describe your methodology.
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Imagine you performed this simulation 100 times. In 15 of the 100 trials of the simulation, none of the 10 passengers chosen was seated in first class.
Does this result provide convincing evidence that the TSA officers did not carry out a truly random selection? Explain your answer.