AP Statistics · Topic 4.11

Parameters for a Binomial Distribution Practice

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

Practice questions

15

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Sample questions

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Sample 1difficulty 2/5
$A scenario must satisfy BINS to be binomial.$
$Which condition is NOT required for a binomial distribution?$
- A
  $Same probability of success$
- B
  $Independent trials$
- C
  $Binary outcome$
- D
  $Trials must occur in a fixed time$
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Why
$BINS = Binary, Independent, Number fixed, Same probability. Time is not required.$
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Sample 2difficulty 2/5
$X ~ Binomial(n = 10, p = 0.2).$
$What is P(X = 0)?$
- A
  $0.0000$
- B
  $0.2000$
- C
  $0.1074$
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- D
  $0.8000$
Why
$P(X=0) = (0.8)^10 \approx 0.1074.$
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Sample 3difficulty 2/5
$X is Binomial(n=20, p=0.3).$
$What is the mean of X?$
- A
  $0.3$
- B
  $6$
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- C
  $20$
- D
  $14$
Why
$Mean = np = 20(0.3) = 6.$
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Sample 4difficulty 3/5
$For X ~ Binomial(n, p), E(X) =$
- A
  $n(1-p)$
- B
  $n + p$
- C
  $p$
- D
  $np$
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Why
$Mean of binomial is np.$
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Sample 5difficulty 3/5
$Flip a fair coin 100 times. Expected number of heads is$
- A
  $25$
- B
  $100$
- C
  $50$
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- D
  $75$
Why
$np = 100 \cdot 0.5 = 50.$
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