Binomial Distribution Questions and Answers

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)=ⁿC_x p^x 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)=ⁿC_x p^x 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) = ⁿC_x p^x q^x
b) P(X = x) = ⁿC_x p^x q^(n-x)
c) P(X = x) = ^xC_n q^x p^(n-x)
d) P(x = x) = ^xC_n pⁿ q^x
View Answer

Answer: b
Explanation: It is the formula for Binomial Distribution that is asked here which is given by P(X = x) = ⁿC_x p^x q^(n-x).

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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 = \(\sqrt{variance} = \sqrt{npq}\).

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 ‘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 ⁿC_x.

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.

8. In a Binomial Distribution, if p = q, then P(X = x) is given by?
a) ⁿC_x (0.5)ⁿ
b) ⁿC_n (0.5)ⁿ
c) ⁿC_x p^(n-x)
d) ⁿC_n p^(n-x)
View Answer

Answer: a
Explanation: If p = q, then p = 0.5
Substituting in P(x)=ⁿC_x p^x q^(n-x) we get ⁿC_n (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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