The Graph, Expectation, and Variance of a Binomial Distribution (VCE SSCE Mathematical Methods): Quizzes

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The Graph, Expectation, and Variance of a Binomial Distribution
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What shape is the binomial distribution graph when p<0.5p < 0.5?

Positively skewed

What shape is the binomial distribution graph when p=0.5p = 0.5?

Symmetrical

What shape is the binomial distribution graph when p>0.5p > 0.5?

Negatively skewed

What is the formula for the expectation of a binomial distribution?

E(X)=npE(X) = np

What is the formula for variance of a binomial distribution?

Var(X)=np(1−p)\text{Var}(X) = np(1-p)

In the binomial variance formula, what does (1−p)(1-p) represent?

Probability of failure

If Var(X)=16\text{Var}(X) = 16, what is the standard deviation σ\sigma?

44

What percentage of outcomes does the interval μ±2σ\mu \pm 2\sigma capture?

Approximately 95%

How are graphs with p=0.2p = 0.2 and p=0.8p = 0.8 related?

They are mirror images

For n=30n = 30 trials with p=13p = \frac{1}{3}, what is E(X)E(X)?

1010

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