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 5 of 14
41. As the normal distribution is symmetrical, its mean, median and mode are:____________?
- A. Coincide
- B. Not equal
- C. Different
- D. None of These
Explanation: Symmetry of the normal curve places its balancing point, middle point, and highest point at the same location. Hence the mean, median, and mode coincide.
Correct answer: Coincide42. In a standard normal distribution z = 0 corresponds to _____________?
- A. Mean
- B. S.D.
- C. M.D.
- D. Q.D.
Explanation: A z-score measures distance from the mean in standard-deviation units, so z=0 means no distance from the mean. It therefore corresponds to the mean, not to the standard deviation or other deviation measures.
Correct answer: Mean43. The range of normal distribution lies between _________?
- A. -∞ to +∞
- B. 0 to ∞
- C. -∞ to 0
- D. None of these
Explanation: A normal random variable can take any real value, although values far from the mean become increasingly unlikely. Therefore, its theoretical range extends from negative infinity to positive infinity.
Correct answer: -∞ to +∞44. Normal distribution has ___________?
- A. 1 parameter
- B. 2 parameter
- C. 3 parameter
- D. 4 parameter
Explanation: A normal distribution is completely specified by two parameters: its mean μ, which fixes the centre, and its variance σ², which controls the spread. Hence it has two parameters.
Correct answer: 2 parameter45. The shape of normal distribution does depend upon _____ and variance?
- A. x
- B. S/σ2
- C. u
- D. 2 µ2
Explanation: The normal distribution is described by its mean μ and variance σ². The mean determines the location of the curve, while the variance determines its spread, so μ fills the blank.
Correct answer: u46. P(µ - σ≤x≤µ + σ)=_________?
- A. .6826
- B. .6743
- C. .6745
- D. .2345
Explanation: About 68.26% of observations in a normal distribution lie within one standard deviation of the mean. Thus P(μ − σ ≤ X ≤ μ + σ) = 0.6826.
Correct answer: .682647. For a normal distribution having µ = 241 and σ = 2 P (X≥235) is:_______?
- A. 0.9986
- B. 0.5
- C. 0.475
- D. 0.235
Explanation: Standardising gives z = (235 − 241)/2 = −3. Therefore P(X ≥ 235) = P(Z ≥ −3) = P(Z ≤ 3) ≈ 0.9986.
Correct answer: 0.998648. Normal distribution has ____shaped?
- A. u-shaped
- B. Bell shaped
- C. T-shaped
- D. Normal shaped
Explanation: A normal curve rises smoothly to one central peak and falls symmetrically on both sides, giving it the familiar bell shape. It is not U-shaped or T-shaped.
Correct answer: Bell shaped49. In normal distribution u2 = S2 and u4 =___________?
- A. 3S2
- B. 3S
- C. 3S4
- D. 4S2/x
Explanation: For a normal distribution, the second central moment is σ² and the fourth central moment is 3σ⁴. Hence μ₄ = 3S⁴ when S denotes the standard deviation.
Correct answer: 3S450. The quartile deviation is ____ (S.D.) is normal dist?
- A. .6734
- B. .7879
- C. .6745
- D. .4567
Explanation: The quartiles of a standard normal distribution occur at z = ±0.6745. Consequently, the quartile deviation is 0.6745 times the standard deviation.
Correct answer: .6745