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CA Foundation Theoretical Distributions — practice questions

Explore 64 free Theoretical Distributions questions in CA Foundation Quantitative Aptitude. Open each question or exercise to read its content, reference answers and available explanation.

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Theoretical Distributions questions and exercises with answers

Showing questions 1–30 of 64.

What does a binomial random variable count?Read the answer and worked solution →With n = 1, the binomial distribution reduces to which case?Read the answer and worked solution →Which pair of parameters fully specifies a binomial distribution?Read the answer and worked solution →Drawing without replacement from a small population gives which distribution?Read the answer and worked solution →When is the binomial a good model for sampling without replacement?Read the answer and worked solution →A binomial variable has mean 12 and variance 8. What is p?Read the answer and worked solution →For n = 8 and p = 0.5, what is the most likely number of successes?Read the answer and worked solution →For n = 9 and p = 0.5, which two values are both most probable?Read the answer and worked solution →For n = 10 and p = 0.3, what is the mode of the binomial?Read the answer and worked solution →When np is an integer, how do binomial mean, median and mode compare?Read the answer and worked solution →A coin shows heads with probability 0.3. P(exactly 4 heads in 6 tosses)?Read the answer and worked solution →A fair coin is tossed 5 times. P(exactly 2 heads) is?Read the answer and worked solution →A machine makes 10% defective items. P(no defective in a sample of 10)?Read the answer and worked solution →A couple has 4 children. P(exactly 2 girls), girl and boy equally likely?Read the answer and worked solution →A quiz has 3 questions with 4 options each. P(exactly one right by guessing)?Read the answer and worked solution →A trial succeeds with probability 0.2, repeated 5 times. P(no success)?Read the answer and worked solution →What is the standard deviation of a binomial with n = 64 and p = 0.5?Read the answer and worked solution →A fair die is rolled 12 times. What is the expected number of sixes?Read the answer and worked solution →Which condition must hold for binomial trials?Read the answer and worked solution →The variance of a binomial B(n, p) equals which expression?Read the answer and worked solution →With n known, how is p estimated from the observed successes?Read the answer and worked solution →A Poisson approximation of B(200, 0.01) uses which value of lambda?Read the answer and worked solution →For large n and small p, the binomial is approximated by which law?Read the answer and worked solution →Which binomial is least suited to a Poisson approximation?Read the answer and worked solution →Which law approximates B(n, p) when n is large enough?Read the answer and worked solution →The normal approximation to B(100, 0.5) has mean and variance of?Read the answer and worked solution →A Poisson distribution gives the probability of what?Read the answer and worked solution →The Poisson parameter lambda equals which quantity?Read the answer and worked solution →Poisson published his probability theory with this distribution in which year?Read the answer and worked solution →Bortkiewicz showed a Poisson fit for which Prussian army data?Read the answer and worked solution →

Worked practice questions

What does a binomial random variable count?

  1. Events in a fixed time interval
  2. Successes in n independent trials
  3. Trials needed for the first success
  4. Values lying below a bell curve
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Correct answer: B. Successes in n independent trials

A binomial variable adds up the successes across a fixed number of independent yes-no trials.

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With n = 1, the binomial distribution reduces to which case?

  1. Bernoulli distribution
  2. Normal distribution
  3. Poisson distribution
  4. Hypergeometric distribution
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Correct answer: A. Bernoulli distribution

One single yes-no trial is exactly a Bernoulli experiment, so the binomial with n = 1 is Bernoulli.

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Which pair of parameters fully specifies a binomial distribution?

  1. Rate and time interval
  2. Trials n and probability p
  3. Mean and sample variance
  4. Mean and standard deviation
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Correct answer: B. Trials n and probability p

The binomial law is written B(n, p), fixed by the number of trials and the success probability.

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More Quantitative Aptitude topics

Time Value of MoneyProbabilityPermutations and CombinationsCorrelation and RegressionRatio and Proportion, Indices and LogarithmsSets, Relations and FunctionsMeasures of Central Tendency and DispersionStatistical Representation of Data and Sampling