Free Probability Distributions MCQs with Answers

• 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.

• 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.

• 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.

• 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…

• 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.

• 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.

• 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 −…

• 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.

• 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.

• 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.

• 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.

• A. Bell
• B. Circle
• C. L
• D. Rectangle

Explanation: A normal distribution is symmetric and mound-shaped, with its familiar outline resembling a bell.

• 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…

• 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.

• 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.

• 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.

• 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.

• 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.

• 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.

• 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.