Free Probability Distributions MCQs with Answers

• 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.

• 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.

• 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.

• 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…

• 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…

• 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.

• 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.

• 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.

• 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.

• 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…

• A. Three
• B. Two
• C. Four
• D. One

Explanation: A normal distribution is determined by two parameters: its mean, which sets the centre, and its variance or standard deviation, which sets…

• A. Continuous
• B. Constant
• C. Discrete
• D. Normal

Explanation: The normal distribution describes a continuous random variable, whose possible values form a continuous range and are represented by areas…

• A. One Outcome
• B. Two Outcome
• C. Three Outcome
• D. Four Outcome

Explanation: A binomial trial has exactly two mutually exclusive outcomes, conventionally called success and failure.

• A. Hypergeometric distribution
• B. Binomial distribution
• C. Poisson distribution
• D. Geometric distribution

Explanation: The hypergeometric distribution models sampling without replacement, so the probability changes from draw to draw.

• A. Independent
• B. Dependent
• C. Collectively Exhaustive
• D. None

Explanation: Hypergeometric trials are dependent because sampling is without replacement, so the outcome of one draw changes the probabilities on later…

• A. n is fixed
• B. Has two outcomes
• C. Trials are independent
• D. Probability of success varies from trial to trial

Explanation: A binomial distribution requires the success probability to remain constant on every trial.

• A. 2
• B. 1
• C. 3
• D. 4
• E. No

Explanation: The standard hypergeometric distribution has three parameters: population size N, number of successes K, and sample size n.

• A. P(X < 0)
• B. P(X = 0)
• C. P(X > 0)
• D. p(0 ≤ X≤ n)

Explanation: A binomial random variable can only take values from 0 through n, so values below zero are impossible and P(X < 0) = 0.

• A. npq
• B. np
• C. √npq
• D. √np
• E. nq-√

Explanation: A binomial variable is the sum of n Bernoulli trials, each having success probability p, so its expected value is np.

• A. Binomial distribution
• B. Geometric distribution
• C. Sampling distribution
• D. Hypergeometrical distributionTry Statistical Software

Explanation: In hypergeometric sampling, items are drawn without replacement, so the composition of the remaining population changes and the success…