Probability and Statistics Questions and Answers – Binomial Distribution

This set of Probability and Statistics Multiple Choice Questions & Answers (MCQs) focuses on “Binomial Distribution”.

1. In a Binomial Distribution, if ā€˜n’ is the number of trials and ā€˜p’ is the probability of success, then the mean value is given by ___________
a) np
b) n
c) p
d) np(1-p)
View Answer

Answer: a
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
µ = 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

Answer: b
Explanation: For a discrete probability function, the variance is given by
Variance (V)=\(\sum_{x=0}^n x^2p(x)-\mu^2\)
Where µ is the mean, substitute P(x)=nCx px q(n-x) in the above equation and put µ = np to obtain
V = npq.

3. If ā€˜X’ is a random variable, taking values ā€˜x’, probability of success and failure being ā€˜p’ and ā€˜q’ respectively and ā€˜n’ trials being conducted, then what is the probability that ā€˜X’ takes values ā€˜x’? 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

Answer: b
Explanation: It is the formula for Binomial Distribution that is asked here which is given by P(X = x) = nCx px q(n-x).
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4. If ā€˜p’, ā€˜q’ and ā€˜n’ 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

Answer: d
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

Answer: b
Explanation: Mean = np
Variance = npq
∓ Mean and Variance are not equal.
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6. It is suitable to use Binomial Distribution only for ___________
a) Large values of ā€˜n’
b) Fractional values of ā€˜n’
c) Small values of ā€˜n’
d) Any value of ā€˜n’
View Answer

Answer: c
Explanation: As the value of ā€˜n’ increases, it becomes difficult and tedious to calculate the value of nCx.

7. For larger values of ā€˜n’, Binomial Distribution ___________
a) loses its discreteness
b) tends to Poisson Distribution
c) stays as it is
d) gives oscillatory values
View Answer

Answer: b
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

Answer: a
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

Answer: b
Explanation: It is applied to a discrete Random variable, hence it is a discrete distribution.
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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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