# Probability and Statistics Questions and Answers – Normal Distribution

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

1. Normal Distribution is applied for ___________
a) Continuous Random Distribution
b) Discrete Random Variable
c) Irregular Random Variable
d) Uncertain Random Variable

Explanation: This is the rule on which Normal distribution is defined, no details on this as of why For more knowledge on this aspect, you can refer to any book or website which speaks on the same.

2. The shape of the Normal Curve is ___________
a) Bell Shaped
b) Flat
c) Circular
d) Spiked

Explanation: Due to the nature of the Probability Mass function, a bell shaped curve is obtained.

3. Normal Distribution is symmetric is about ___________
a) Variance
b) Mean
c) Standard deviation
d) Covariance

Explanation: Due to the very nature of p.m.f of Normal Distribution, the graph appears such that it is symmetric about its mean.

4. For a standard normal variate, the value of mean is?
a) ∞
b) 1
c) 0
d) not defined

Explanation: For a normal variate, if its mean = 0 and standard deviation = 1, then its called as Standard Normal Variate. Here, the converse is asked.

5. The area under a standard normal curve is?
a) 0
b) 1
c) ∞
d) not defined

Explanation: For any probability distribution, the sum of all probabilities is 1. Area under normal curve refers to sum of all probabilities.

6. The standard normal curve is symmetric about the value ___________
a) 0.5
b) 1
c) ∞
d) 0

Explanation: Normal curve is always symmetric about mean, for standard normal curve or variate mean = 0.

7. For a standard normal variate, the value of Standard Deviation is ___________
a) 0
b) 1
c) ∞
d) not defined

Explanation: If the mean and standard deviation of a normal variate are 0 and 1 respectively, it is called as standard normal variate. Here the converse is asked.

8. Normal Distribution is also known as ___________
a) Cauchy’s Distribution
b) Laplacian Distribution
c) Gaussian Distribution
d) Lagrangian Distribution

Explanation: Named after the one who proposed it. For further details, refer to books or internet.

9. Skewness of Normal distribution is ___________
a) Negative
b) Positive
c) 0
d) Undefined

Explanation: Since the normal curve is symmetric about its mean, its skewness is zero. This is a theoretical explanation for mathematical proofs, you can refer to books or websites that speak on the same in detail.

10. For a normal distribution its mean, median, mode are equal.
a) True
b) False

Explanation: It has a theoretical evidence that requires some serious background on several topics For more details you can refer to any book or website that speaks on the same.

11. In Normal distribution, the highest value of ordinate occurs at ___________
a) Mean
b) Variance
c) Extremes
d) Same value occurs at all points

Explanation: This is due the behaviour of the pdf of Normal distribution.

12. The shape of the normal curve depends on its ___________
a) Mean deviation
b) Standard deviation
c) Quartile deviation
d) Correlation

Explanation: This can be seen in the pdf of normal distribution where standard deviation is a variable.

13. The value of constant ‘e’ appearing in normal distribution is ___________
a) 2.5185
b) 2.7836
c) 2.1783
d) 2.7183

Explanation: This is a standard constant.

14. In Standard normal distribution, the value of mode is ___________
a) 2
b) 1
c) 0
d) Not fixed

Explanation: In a standard normal distribution, the value of mean is 0 and in normal distribution mean and mode coincide.

15. In Standard normal distribution, the value of median is ___________
a) 1
b) 0
c) 2
d) Not fixed

Explanation: In a standard normal distribution the value of mean is o and in normal distribution mean, median and mode coincide.

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