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Statistics and probability

Course: Statistics and probability > Unit 9

Lesson 6: Binomial mean and standard deviation formulas
Math
Statistics and probability
Random variables
Binomial mean and standard deviation formulas
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Mean and standard deviation of a binomial random variable

AP.STATS: UNC‑3 (EU), UNC‑3.C (LO), UNC‑3.C.1 (EK)
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Problem

Ms. Davis is doing an activity with her statistics students where she gives them a 20-question multiple choice test, and they know none of the answers. Students need to guess on every question, and each question has 5 possible choices, 1 of which is correct.
What are the mean and standard deviation of the number of questions that each student gets correct?
You may round your answers to the nearest tenth.
mean:
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
correct
standard deviation:
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
correct
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