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 8 of 14
71. If p= 0.1 and n = 400 then mean _______________?
- A. 60
- B. 30
- C. 20
- D. 40
Explanation: The binomial mean is np, so the mean is 400 × 0.1 = 40. This makes option (d) correct.
Correct answer: 4072. Binomial distribution ranges from _______________?
- A. 1 to n
- B. 0 to n
- C. 1 to ∞
- D. 0 to ∞
Explanation: For a binomial variable, the number of successes can be as low as 0 and as high as all n trials, so its range is 0 to n.
Correct answer: 0 to n73. Binomial distribution is positively skewed when ______________?
- A. p > q
- B. P = q
- C. p < q
- D. P/q
Explanation: A binomial distribution is positively skewed when successes are less likely than failures, meaning p<q. When p=q it is symmetrical, while p>q produces negative skewness.
Correct answer: p < q74. In binomial experiment, the experiment is repeated ______________?
- A. n; fixed number of times
- B. a large number times
- C. n; where n < 0
- D. n = 100
Explanation: A binomial experiment consists of n independent trials, where n is a fixed positive integer. The number of repetitions is not necessarily large and cannot be negative.
Correct answer: n; fixed number of times75. In binomial distribution with ________ trials mean is np and variance is npq?
- A. Dependent
- B. Independent
- C. Linear
- D. Equal
Explanation: The formulas mean=np and variance=npq apply when the n Bernoulli trials are independent and have the same success probability p. Dependence would generally change the variance formula.
Correct answer: Independent76. Mean of the binomial distribution is ______________?
- A. Pq
- B. nP
- C. xm
- D. Non of these
Explanation: The binomial mean equals the expected number of successes, calculated as the number of trials multiplied by the success probability: E(X)=np.
Correct answer: nP77. The mean of a binomial distribution is always:____________________?
- A. Equal to variance
- B. Less than variance
- C. Greater than varince
- D. None of these
Explanation: The binomial mean is np and its variance is npq. Since 0<q<1 in the standard case, np is greater than npq, so the mean is greater than the variance.
Correct answer: Greater than varince78. Binomial distribution has _______ parameter?
- A. 4
- B. 3
- C. 2
- D. 6
Explanation: A binomial distribution is determined by two parameters: n, the number of trials, and p, the probability of success on each trial. Thus, it has two parameters.
Correct answer: 279. Successive trials in binomial distribution are:__________________?
- A. Dependent
- B. Independent
- C. Equally Likely
- D. Mutually exclusive
- E. Non
Explanation: The trials in a binomial experiment are independent, meaning the outcome of one trial does not change the probability of success on another. They must also have the same success probability.
Correct answer: Independent80. A random variable X has binomial distribution with n = 10 and p = 0.3 then variance of X is:_____________________?
- A. 10
- B. 12
- C. 2.1
- D. 21
- E. None
Explanation: For a binomial variable, variance is npq, where q = 1 - p. Here, npq = 10(0.3)(0.7) = 2.1.
Correct answer: 2.1