This set of Probability and Statistics Multiple Choice Questions & Answers (MCQs) focuses on “Binomial Distribution”.
1. In a Binomial Distribution, if ānā is the number of trials and āpā is the probability of success, then the mean value is given by ___________
a) np
b) n
c) p
d) np(1-p)
View Answer
Explanation: For a discrete probability function, the mean value or the expected value is given by
Mean (μ)=\(\sum_{x=0}^{n}xp(x)\)
For Binomial Distribution P(x)=nCx px q(n-x), substitute in above equation and solve to get
Āµ = np.
2. In a Binomial Distribution, if p, q and n are probability of success, failure and number of trials respectively then variance is given by ___________
a) np
b) npq
c) np2q
d) npq2
View Answer
Explanation: For a discrete probability function, the variance is given by
Variance (V)=\(\sum_{x=0}^n x^2p(x)-\mu^2\)
Where Āµ is the mean, substitute P(x)=nCx px q(n-x) in the above equation and put Āµ = np to obtain
V = npq.
3. If āXā is a random variable, taking values āxā, probability of success and failure being āpā and āqā respectively and ānā trials being conducted, then what is the probability that āXā takes values āxā? Use Binomial Distribution
a) P(X = x) = nCx px qx
b) P(X = x) = nCx px q(n-x)
c) P(X = x) = xCn qx p(n-x)
d) P(x = x) = xCn pn qx
View Answer
Explanation: It is the formula for Binomial Distribution that is asked here which is given by P(X = x) = nCx px q(n-x).
4. If āpā, āqā and ānā are probability pf success, failure and number of trials respectively in a Binomial Distribution, what is its Standard Deviation?
a) \(\sqrt{np}\)
b) \(\sqrt{pq}\)
c) (np)2
d) \(\sqrt{npq}\)
View Answer
Explanation: The variance (V) for a Binomial Distribution is given by V = npq
Standard Deviation = \(\sqrt{variance} = \sqrt{npq}\).
5. In a Binomial Distribution, the mean and variance are equal.
a) True
b) False
View Answer
Explanation: Mean = np
Variance = npq
ā“ Mean and Variance are not equal.
6. It is suitable to use Binomial Distribution only for ___________
a) Large values of ānā
b) Fractional values of ānā
c) Small values of ānā
d) Any value of ānā
View Answer
Explanation: As the value of ānā increases, it becomes difficult and tedious to calculate the value of nCx.
7. For larger values of ānā, Binomial Distribution ___________
a) loses its discreteness
b) tends to Poisson Distribution
c) stays as it is
d) gives oscillatory values
View Answer
Explanation: P(x)=\(\lim_{n\rightarrow\infty}c_x^n p^x q^{n-x}=\frac{e^{-m}m^x}{x!}\)
Where m = np is the mean of Poisson Distribution.
8. In a Binomial Distribution, if p = q, then P(X = x) is given by?
a) nCx (0.5)n
b) nCn (0.5)n
c) nCx p(n-x)
d) nCn p(n-x)
View Answer
Explanation: If p = q, then p = 0.5
Substituting in P(x)=nCx px q(n-x) we get nCn (0.5)n.
9. Binomial Distribution is a ___________
a) Continuous distribution
b) Discrete distribution
c) Irregular distribution
d) Not a Probability distribution
View Answer
Explanation: It is applied to a discrete Random variable, hence it is a discrete distribution.
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