Passing the Test 9 Copyright © 2026 Pearson Education, Inc. Passing the Test (50 – 60 minutes) Learning Objective(s): Students will be able to solve real-world problems involving binomial distributions. Students will be able to calculate the expected value and standard deviation of a binomial distribution. Materials needed: Student pages: Passing the Test Calculator Lesson Procedure: Warm–Up 10 minutes Prompt: What are examples of situations that represent binomial distributions? In which of these situations could statistics be useful? Discuss: binomial distributions, statistics and its usefulness Guided Instruction 15 minutes Present: scenario for Passing the Test. Example: A coin flip has two outcomes. If you flip it 10 times to determine the frequency of heads, what is p? 0.5 What is q? 0.5 What is n? 10 What is the expected value? 5 What is the standard deviation? 1.58 Flip a coin 10 times and record your results. How likely is your result? If the result is outside of 2 standard deviations, it is quite unlikely (0, 1, 9, or 10 heads). Review: key terms –binomial distribution, standard deviation binomial distribution: a probability distribution summarizing the likelihood of one of two outcomes a certain number of times in a certain number of independent trials with the same probability standard deviation: a value that shows the amount of variation of a set of values from its mean Independent Practice 20 minutes Distribute: student activity Passing the Test Allow students to work individually or in pairs. Have students support each other during the activity. Remind students to use feedback to improve their calculations, recognizing errors and making new suggestions. Remind students to be courteous and use classroom-appropriate language. Closure 10–15 minutes Review Answers: 1. 0.84; the probability of success (passing) 2. 120; the number of students taking the exam (independent events) 3. 0.16; the probability of failing 4. Yes; a. np and nq are both greater than or equal to 5; b. 101; c. 4 5. 101 6. The expected value,101, is the number of students who will likely pass the final exam. 7. a. No; this is outside 3 standard deviations; b. Examples could include a higher-than-normal experience level or studying level among this group of students, cheating, or better teaching by the professor. Discuss: In what other situations could standard deviation be used to determine whether results are likely?
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