Free Probability Distributions MCQs with Answers
132 Probability Distributions MCQs from Statistics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
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132 questions · page 9 of 14
81. If in a binomial distribution n = 1 then E(X) is:____________________?
- A. q
- B. p
- C. 0
- D. 1
Explanation: The binomial mean is E(X) = np. When n = 1, E(X) = 1 × p = p, which is also the mean of a Bernoulli variable.
Correct answer: p82. The mean, median and mode for binomial distribution will be equal when:______________?
- A. p= 0.5
- B. P 0.5
- C. p = 1
- D. None of these
Explanation: When p = 0.5, the binomial distribution is symmetric, so its mean and median coincide, and in the usual textbook treatment the mode is also taken at the centre. Thus, the intended answer is p = 0.5.
Correct answer: p= 0.583. Binomial distribution is negatively skewed when:__________________?
- A. p=0
- B. p>1/2
- C. p=1/2
- D. p=1/3
Explanation: A binomial distribution is negatively skewed when successes are more likely than failures, so p > 0.5. When p = 0.5 it is symmetric, while p < 0.5 produces positive skewness.
Correct answer: p>1/284. Binomial distribution has parameters:______________?
- A. Three
- B. Two
- C. One
- D. Four
- E. None
Explanation: The binomial distribution has two parameters: n, the number of trials, and p, the probability of success. The failure probability q is determined by p because q = 1 - p.
Correct answer: Two85. The variance of binomial distribution is always:________________?
- A. Less than mean
- B. Equal to mean
- C. Greater than mean
- D. Equal to standard deviation
- E. None of these
Explanation: For a binomial distribution, mean = np while variance = npq. Since q is less than 1 for a non-degenerate binomial distribution, npq is less than np, so the variance is less than the mean.
Correct answer: Less than mean86. Binomial distribution is symmetrical when:_________________?
- A. p = q
- B. p > q
- C. p > q
- D. np > npq
Explanation: A binomial distribution is symmetrical when the success and failure probabilities are equal, so p = q = 0.5. When p and q differ, the distribution becomes skewed.
Correct answer: p = q87. The successive trials are with replacement in:________________?
- A. Hpergeometric distribution
- B. Binomial distribution
- C. Geometric distribution
- D. None of these
Explanation: In a binomial model, each trial has the same success probability because trials are independent, as when sampling with replacement. Hypergeometric sampling instead uses sampling without replacement.
Correct answer: Binomial distribution88. Which of the following is not a condition of the binomial distribution ?
- A. Only 2 possible outcomes
- B. Have constant probability
- C. Must have at least 3 trials
- D. Trials must be independent
Explanation: A binomial distribution does not require at least three trials; it can be defined for any positive integer n, including one trial. It does require two outcomes, constant probability, and independent trials.
Correct answer: Must have at least 3 trials89. In a binomial distribution, n = 20 and p = 3/5, then variance of this distribution ______________?
- A. 60
- B. 12
- C. 4.8
- D. 0
Explanation: The binomial variance is npq, where q = 1 - p = 2/5. Thus, variance = 20 × 3/5 × 2/5 = 4.8.
Correct answer: 4.890. What is the variance of binomial distribution __________________?
- A. n p
- B. np (1 - p)
- C. np/q
- D. nq/p
Explanation: For a binomial distribution, q represents the failure probability and equals 1 - p. The variance is therefore npq = np(1 - p).
Correct answer: np (1 - p)