# Probability and Statistics Questions and Answers – Binomial Distribution

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

1. In a Binomial Distribution, if ‘n’ is the number of trials and ‘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.
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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 ‘X’ is a random variable, taking values ‘x’, probability of success and failure being ‘p’ and ‘q’ respectively and ‘n’ trials being conducted, then what is the probability that ‘X’ takes values ‘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).

4. If ‘p’, ‘q’ and ‘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 = $$\sqrt{variance} = \sqrt{npq}$$.
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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.

6. It is suitable to use Binomial Distribution only for ___________
a) Large values of ‘n’
b) Fractional values of ‘n’
c) Small values of ‘n’
d) Any value of ‘n’
View Answer

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

7. For larger values of ‘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.
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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 is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn