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 4 of 14
31. In a normal distribution E(X-µ)2 is________________?
- A. Variance
- B. Mean Deviation
- C. Standard Deviation
- D. Quartile Deviation
Explanation: The second central moment is E[(X − μ)²], which by definition is the variance. Standard deviation is its square root, not the moment itself.
Correct answer: Variance32. Shape of normal curve can be related to_______________?
- A. Bell
- B. Circle
- C. L
- D. Rectangle
Explanation: A normal distribution is symmetric and mound-shaped, with its familiar outline resembling a bell. The other shapes do not describe its probability density curve.
Correct answer: Bell33. We use normal distribution when "n" is________________?
- A. Small
- B. None
- C. Fixed
- D. Large
Explanation: The normal distribution is commonly used as an approximation for sampling distributions when the sample size n is large, because of the central limit theorem. Small samples may require other distributions, such as t, depending on the conditions.
Correct answer: Large34. The lower and upper quartile of standard normal variation are respectively ?
- A. µ+0.6745σ and µ-0.6745σ
- B. -0.6745 and 0.6745
- C. -0.7979 and 0.7979
- D. -0.7979σ and 0.7979σ
Explanation: The standard normal first and third quartiles have z-values −0.6745 and 0.6745, respectively. Since the distribution is standardised, these values are not multiplied by σ.
Correct answer: -0.6745 and 0.674535. If X N(55,49) then σ ?
- A. 7
- B. 55
- C. 104
- D. 49
Explanation: In the usual notation N(μ, σ²), N(55, 49) gives σ² = 49. Taking the square root yields σ = 7.
Correct answer: 736. The normal distribution is_________?
- A. Platykurtic
- B. Leptokurtic
- C. Mesoukurtic
- D. None of these
Explanation: The normal curve has kurtosis β₂=3, which is the reference level called mesokurtic. Platykurtic curves are flatter, while leptokurtic curves are more peaked than normal.
Correct answer: Mesoukurtic37. In normal distribution Q.D. ( quartile deviation)is equal to________?
- A. σ
- B. 0.7979 σ
- C. 0.6745 σ
- D. None of these
Explanation: For a normal distribution, Q1 and Q3 occur at z=−0.6745 and z=+0.6745, so half their difference is Q.D.=0.6745σ. Thus the quartile deviation is smaller than the standard deviation.
Correct answer: 0.6745 σ38. P95 means _____?
- A. The central 95% area
- B. The point above above which95% area lies
- C. The point above below which 95% area lies
- D. Both (a) and (b) but not (c)
Explanation: P95 is the 95th percentile, the value below which 95% of observations lie. It is therefore not the central 95% interval, which would require two boundary points.
Correct answer: The point above below which 95% area lies39. If β1 = 0 it means the distribution is _______________?
- A. Symmetrical
- B. + vely skewed
- C. -vely skewed
- D. Non of these
Explanation: β₁ is the squared measure of skewness, so β₁=0 indicates zero skewness and is conventionally described as a symmetrical distribution. Positive or negative skewness would produce a positive value of β₁, not distinguish its direction.
Correct answer: Symmetrical40. The maximum of function is at_______________?
- A. X = σ2
- B. X = µ
- C. X = µ + σ
- D. X = 0
Explanation: The normal density is highest at its centre, and its centre is the mean μ. At μ, the exponential term in the density is largest because the squared distance from μ is zero.
Correct answer: X = µ