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 10 of 14
91. The sum of p and q is always:___________________?
- A. 0
- B. 2
- C. 1
- D. None of these
Explanation: In a binomial distribution, p is the success probability and q is the failure probability, with q = 1 - p. Therefore, p + q = 1.
Correct answer: 192. If in binomial distribution p ≠ q, the distribution is:___________________?
- A. Positively skewed
- B. Negative skewed
- C. May be positive skewed or negative skewed.
- D. None of these
Explanation: The binomial skewness has the sign of q - p. It is positively skewed when p < q and negatively skewed when p > q, so either direction is possible when p ≠ q.
Correct answer: May be positive skewed or negative skewed.93. The binomial distribution is positively skewed when:________________?
- A. p > q
- B. p < q
- C. p = q
- D. both (a) and (b
Explanation: For a binomial distribution, positive skewness occurs when p is smaller than q, or p < 0.5. When p > q, the distribution is negatively skewed, while p = q gives symmetry.
Correct answer: p < q94. If 5 dice are rolled 96 times then N. =___________?
- A. 5
- B. 96
- C. 5/96
- D. 96/5
Explanation: N denotes the number of repetitions of the experiment. Rolling five dice 96 times means the experiment is repeated 96 times, so N = 96.
Correct answer: 9695. If a Binomial experiment is repeated 'N' times then binomial frequency distribution is. _______________?
- A. N.{nx}px qn-x
- B. N p q
- C. N.{n/x}px qn-x
- D. N.{n/x}p qn-x
Explanation: The binomial frequency for x successes is N multiplied by the binomial probability, namely N·C(n,x)·p^x·q^(n−x). Option a is the intended form, despite the compressed notation.
Correct answer: N.{nx}px qn-x96. For a binomial distribution?
- A. n must assume a number between 1 and 20 or 25
- B. p must be a multiple of 10
- C. There must be at least 3 possible outcomes
- D. None of these
Explanation: A binomial experiment requires a fixed number of trials, two possible outcomes per trial, and constant success probability, but n is not restricted to 20 or 25 and p need not be a multiple of 10. Therefore none of the listed statements is required.
Correct answer: None of these97. If _________ then the distribution is positively skewed?
- A. p < q
- B. q/p
- C. p > q
- D. p > 1/2
Explanation: Positive skewness in a binomial distribution occurs when failures are more probable than successes, so q > p or p < q. The condition p > q produces negative skewness.
Correct answer: p < q98. Which of the following is not a requirement for binomial distribution ?
- A. Constant Probability of Success
- B. Only two possible outcomes
- C. A fixed number of trials
- D. Equally likely outcomes
Explanation: The two outcomes need not be equally likely; they may have probabilities p and q with p different from q. Equal probabilities are required only for a symmetric binomial distribution, not every binomial distribution.
Correct answer: Equally likely outcomes99. If u = 5 and S.D. = 2.5 then Binomial distribution are ________________?
- A. Unequal
- B. Wrong
- C. Fair
- D. None of these
Explanation: For a binomial distribution, mean = np and variance = npq, so variance divided by mean must equal q. Here q = 2.5²/5 = 1.25, which is impossible because a probability cannot exceed 1; hence the stated values are invalid.
Correct answer: Wrong100. Binomial distribution is symmetrical when P=_________________?
- A. 1/q
- B. 1
- C. q
- D. 2q
Explanation: Symmetry occurs when the success and failure probabilities are equal, p = q. Since p + q = 1, this means p = q = 1/2, making option c correct.
Correct answer: q