Which scenario is binomial?

Answer: Number of heads in 20 fair coin flips 20 trials, fixed n, binary outcomes, independent, constant p = 0.5. Binomial.

Which is NOT a requirement of a binomial setting?

Answer: Number of successes is random AND p varies between trials Binomial requires constant p; varying p is a violation.

AP Statistics · Topic 4.10

Introduction to the Binomial Distribution Practice

Part of Probability, Random Variables, and Probability Distributions.(UNC-3.A)

Practice questions

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Sample questions

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Sample 1difficulty 2/5
$A study sets a binomial distribution.$
$Which scenario is binomial?$
- A
  $Time until first head$
- B
  $Number of cards drawn until first ace$
- C
  $Number of heads in 20 fair coin flips$
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- D
  $Outcome of one die roll$
Why
$20 trials, fixed n, binary outcomes, independent, constant p = 0.5. Binomial.$
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Sample 2difficulty 3/5
$n=20, p=0.30 binomial: mean \approx$
- A
  $9$
- B
  $14$
- C
  $6$
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- D
  $3$
Why
$np = 20 \cdot 0.30 = 6.$
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Sample 3difficulty 3/5
$Which is NOT a requirement of a binomial setting?$
- A
  $Number of successes is random AND p varies between trials$
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- B
  $Independent trials$
- C
  $Fixed number of trials$
- D
  $Two outcomes per trial (success/failure)$
Why
$Binomial requires constant p; varying p is a violation.$
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Sample 4difficulty 3/5
$Consider sampling 50 voters with replacement and counting Republicans.$
$Why is this binomial?$
- A
  $Counts outcomes that are normally distributed$
- B
  $Sample size large enough$
- C
  $Because it follows the empirical rule$
- D
  $Fixed n, binary, independent (with replacement), constant p$
  check_circle
Why
$BINS: 50 fixed trials, R/not-R, with replacement = independent, p constant.$
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Sample 5difficulty 3/5
$A symmetric binomial bar chart suggests p =$
- A
  $0.9$
- B
  $0.5$
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- C
  $0.1$
- D
  $0.3$
Why
$Symmetry of binomial occurs at p = 0.5.$
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