Binomial Distribution Quiz
The question sheet
Reveal any answer as you study-
How many characteristics does a binomial experiment have?
- Two
- Three
- Four
- Five
Reveal answer
Answer: Three
Source evidence
PDF page 261: There are three characteristics of a binomial experiment.
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In a binomial experiment, what does p + q equal?
- 0.5
- 0
- 2
- 1
Reveal answer
Answer: 1
Source evidence
PDF page 261: of a success on one trial, and q denotes the probability of a failure on one trial. p + q = 1.
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In a binomial experiment, q denotes the probability of what?
- A failure
- A trial
- A sample
- A success
Reveal answer
Answer: A failure
Source evidence
PDF page 261: of a success on one trial, and q denotes the probability of a failure on one trial. p + q = 1.
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For a binomial experiment, the random variable X is defined as:
- The number of trials
- The mean of the distribution
- The probability of success
- The number of successes in n trials
Reveal answer
Answer: The number of successes in n trials
Source evidence
PDF page 262: 0.6) and his probability of failure (q = 0.4) remain the same. The outcomes of a binomial experiment fit a binomial probability distribution. The random variable X = the number of successes obtained in the n independent trials.
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The variance of a binomial probability distribution equals:
- np
- np + q
- p + q
- npq
Reveal answer
Answer: npq
Source evidence
PDF page 262: The mean, μ, and variance, σ , for the binomial probability distribution are μ = np and σ = npq. The standard deviation, σ,
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An experiment with characteristics two and three where n = 1 is called a:
- Sample trial
- Binomial trial
- Bernoulli Trial
- Poisson trial
Reveal answer
Answer: Bernoulli Trial
Source evidence
PDF page 262: Any experiment that has characteristics two and three and where n = 1 is called a Bernoulli Trial (named after Jacob Bernoulli who, in the late 1600s, studied them extensively). A binomial experiment takes place when the number of successes is counted in one or more Bernoulli Trials.
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Who studied Bernoulli Trials extensively in the late 1600s?
- Jacob Bernoulli
- William Gosset
- Isaac Newton
- Carl Gauss
Reveal answer
Answer: Jacob Bernoulli
Source evidence
PDF page 262: Any experiment that has characteristics two and three and where n = 1 is called a Bernoulli Trial (named after Jacob Bernoulli who, in the late 1600s, studied them extensively). A binomial experiment takes place when the number of successes is counted in one or more Bernoulli Trials.
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In the win-lose game played 20 times with 55% win probability, p equals:
- 0.55
- 0.20
- 0.15
- 0.45
Reveal answer
Answer: 0.55
Source evidence
PDF page 262: Suppose you play a game that you can only either win or lose. The probability that you win any game is 55%, and the probability that you lose is 45%. Each game you play is independent. If you play the game 20 times, write the function that describes the probability that you win 15 of the 20 times. Here, if you define X as the number of wins, then X takes on the values 0, 1, 2, 3, ..., 20. The probability of a success is p = 0.55. The probability of a
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For X ~ B(n, p), what does n represent?
- Number of successes
- Probability of success
- Number of trials
- Probability of failure
Reveal answer
Answer: Number of trials
Source evidence
PDF page 264: X ~ B(n, p) Read this as "X is a random variable with a binomial distribution." The parameters are n and p; n = number of trials, p = probability of a success on each trial.
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For the adult workers example, X ~ B(20, 0.41). What is q?
- 0.59
- 0.12
- 0.41
- 0.20
Reveal answer
Answer: 0.59
Source evidence
PDF page 264: X takes on the values 0, 1, 2, ..., 20 where n = 20, p = 0.41, and q = 1 – 0.41 = 0.59. X ~ B(20, 0.41)
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Which TI command calculates P(x ≤ value) for a binomial?
- binomcdf
- normalcdf
- binompdf
- invNorm
Reveal answer
Answer: binomcdf
Source evidence
PDF page 264: Go into 2 DISTR. The syntax for the instructions are as follows: To calculate (x = value): binompdf(n, p, number) if "number" is left out, the result is the binomial probability table. To calculate P(x ≤ value): binomcdf(n, p, number) if "number" is left out, the result is the cumulative binomial probability table.
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For X ~ B(20, 0.41), the expected number of workers (mean) is:
- 12
- 8.2
- 20
- 2.20
Reveal answer
Answer: 8.2
Source evidence
PDF page 265: is the mean, μ = np = (20)(0.41) = 8.2.
Introductory Statistics
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