Florida B.E.S.T. MA.912.DP.6.4
The Standard
Given a binomial distribution, calculate and interpret the expected value. Solve real-world problems involving binomial distributions.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students model repeated independent trials with two possible outcomes and a constant success probability. They calculate np, interpret it as a long-run average, and use binomial probabilities to answer context-based questions.
What Mastery Looks Like
- Students identify n, p, and the requested number of successes from a situation. They calculate expected value with np, find a binomial probability, and explain each result using the problem context.
Common Misconceptions
- Students may use np as the probability of success rather than the long-run average number of successes. They may confuse n with x, omit combinations, or assume trials are independent when they are not.
How to Assess It
- Give this exit ticket: “A player makes 70% of 10 free throws. Find the expected number made and the probability of exactly 8 makes. Interpret both answers.”
Lesson moves
Ways to Teach It
Flip a coin 10 times, record heads, repeat in groups, and compare the class average with the expected value.
Ask students to explain why an expected value of 7.5 successes does not mean one trial can produce 7.5 successes.
Play binomial match-up with cards showing scenarios, values of n and p, expected values, and probabilities for students to pair.
Use a quality-control problem to predict defective items in a shipment and calculate the probability of finding a specified number.
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