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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21. The standardized normal variate z means_________ away from the mean?
- A. Mean
- B. S.D.
- C. Variance
- D. None of these
Explanation: The standardized normal variate is z = (x − μ)/σ, so it measures the distance from the mean in standard-deviation units. Thus z = 1 means one standard deviation above the mean, while z = −1 means one below it.
Correct answer: S.D.22. In a normal distribution, what is the z score associated with the mode ?
- A. -1
- B. 0
- C. +1
- D. None of these
Explanation: A normal distribution is symmetric, with mean, median, and mode all equal to μ. Therefore, at the mode, z = (μ − μ)/σ = 0.
Correct answer: 023. If X ˜ N (µ, σ2) then Z ˜__________?
- A. N(0, σ2)
- B. N(1, σ2)
- C. N(0, 1)
- D. N(1, 1)
Explanation: Standardizing X by subtracting μ and dividing by σ gives Z = (X − μ)/σ, which has mean 0 and variance 1. Hence Z follows N(0, 1), not a distribution retaining μ or σ².
Correct answer: N(0, 1)24. Normal distribution is the distribution of _______________?
- A. Discrete r.v.
- B. Continuous r.v.
- C. Qualitative variable
- D. Quantitative variable
Explanation: The normal distribution is continuous because its variable can take any value over an interval and probabilities are represented by areas under its curve. It is also quantitative, but continuous random variable is the more specific choice.
Correct answer: Continuous r.v.25. In normal distribution, mean ______= Mode?
- A. Quartile
- B. Mean deviation
- C. Median
- D. S.D.
Explanation: The normal curve is symmetric and unimodal, so its mean, median, and mode coincide. Therefore, the mean is equal to the median as well as the mode.
Correct answer: Median26. Area of normal distribution total is equal to _______?
- A. Two
- B. One
- C. Four
- D. Three
Explanation: The total area under any probability density curve represents the probability of all possible outcomes, which is 1. For a normal curve, the two tails and central region together therefore have area one.
Correct answer: One27. Standard normal variable Z is___________?
- A. x - µ /σ
- B. µ- x /σ
- C. σ - x/ µ
- D. x - σ/ µ
Explanation: The standard normal variable is obtained by measuring X's deviation from the mean and expressing it in standard-deviation units: Z = (X − μ)/σ. Reversing the subtraction changes the sign and is not the standard definition.
Correct answer: x - µ /σ28. In normal distribution Q1=_________?
- A. u + .6745 (S.D.)
- B. u - .7979 (S.D.)
- C. u + .6745 (S.D.)
- D. u - .6745 (S.D.)
Explanation: The first quartile is the 25th percentile, whose standard-normal z value is about −0.6745. Converting back gives Q1 = μ − 0.6745σ, whereas the positive value gives Q3.
Correct answer: u - .6745 (S.D.)29. If n ≥ 30 and _____ then binomial approaches to normal distribution?
- A. q/p
- B. p = q
- C. pq
- D. p = n
Explanation: When p = q = 0.5 and n is at least 30, both np and nq are sufficiently large, making the binomial distribution reasonably close to normal. More generally, the approximation is judged by np and nq rather than by p = q alone.
Correct answer: p = q30. In a normal distribution quartile deviation is _______ (S.D.)?
- A. .2745
- B. .3789
- C. .79079
- D. .6745
Explanation: For a normal distribution, the first and third quartiles lie at z = −0.6745 and z = 0.6745. Thus the quartile deviation is 0.6745 standard deviations, making option d correct.
Correct answer: .6745