Normal Distribution MCQ Multiple Choice Questions Answers | Quiz for Practice

Q: 2. For the standard normal distribution, P(Z > mean) is:

Correct Answer is: Equal to 0.5

Q: 7. If X is a normal random variable having mean μ, then E|X - μ| is equal to:

Correct Answer is: Mean deviation

Q: 12. In a normal curve, the highest point on the curve occurs at the mean, μ, which is also the:

Correct Answer is: Median and mode

Q: 16. In a normal probability distribution of a continuous random variable, the value of standard deviation is:

Correct Answer is: Greater than zero

Q: 18. In a standard normal distribution, the value of mode is:

Correct Answer is: Equal to zero

Q: 19. In normal distribution:

Correct Answer is: Mean = Median = Mode

Normal Distribution Multiple Choice Questions (MCQs) are essential practice tools for students and exam aspirants. These questions help you understand and apply the concepts of normal distribution, a fundamental topic in statistics and probability.

About Normal Distribution MCQ Questions

Normal Distribution, also known as the Gaussian Distribution, is a continuous probability distribution that is symmetrically distributed around the mean. Key concepts covered in these MCQs include the properties of the normal curve, standard deviation, z-scores, and how to calculate probabilities using the standard normal table.

Why Practice Normal Distribution Objective Questions?

Practicing Normal Distribution MCQs offers several benefits. It helps you prepare for school and college exams, enhances your understanding of statistical concepts, and improves your problem-solving skills. Additionally, these questions are useful for competitive exams and job interviews, where knowledge of probability and statistics is often required.

Who Should Use These MCQs?

Students preparing for school or college exams
Competitive exam aspirants
Candidates preparing for interviews

Normal Distribution MCQ Questions for Practice

1. A random variable X is normally distributed with μ = 70 and σ² = 25. The third moment about arithmetic mean is:

Zero
Less than zero
Greater than zero
None of the above

2. For the standard normal distribution, P(Z > mean) is:

More than 0.5
Less than 0.5
Equal to 0.5
Difficult to tell

3. Given a standardized normal distribution (with a mean of zero and a standard deviation of one), P(Z < variance) is equal to:

0.8413
0.3413
0.1587
0.5

4. If X ~ N(μ,σ²), the points of inflection of normal distribution are:

±σ
±μ
σ ± μ
μ ± σ

5. If X ~ N(μ,σ²), the standard normal variate is distributed as:

N(1,0)
N(0,1)
N(μ,0)
N(0,σ²)

6. If X is a normal random variable having mean μ, then E(X - μ)² is equal to:

σ²
σ
3σ⁴
β₁

7. If X is a normal random variable having mean μ, then E|X - μ| is equal to:

Variance
Standard deviation
Quartile deviation
Mean deviation

8. If X~N(100, 64), then standard deviation σ is:

100
64
8
100 - 64 = 36

9. If Z~N, the coefficient of variation is equal to:

Zero
One
Infinity
Hundred percent

10. If Z~N, then μ₄ is equal to:

1
3
σ⁴

11. In a normal curve μ ± 0.6745σ covers:

50% area
68.27% area
95.45% area
99.73% area

12. In a normal curve, the highest point on the curve occurs at the mean, μ, which is also the:

Median and mode
Geometric mean and harmonic mean
Lower and upper quartiles
Variance and standard deviation

13. In a normal curve, the ordinate is highest at:

Mean
Variance
Standard deviation
Q1

14. In a normal distribution whose mean is land standard deviation 0, the value 4 quartile deviation is approximately:

(4/5)
4/5 σ
2/3 σ
(2/3)

15. In a normal distribution, the lower and upper quartiles are equidistant from the mean and are at a distance of:

0.7979
0.7979 σ
0.6745
0.6745 σ

16. In a normal probability distribution of a continuous random variable, the value of standard deviation is:

Zero
Less than zero
Greater than zero
None of the above

17. In a standard normal distribution, the area to the left of Z = 1 is :

0.6413
0.7413
0.8413
0.3413

18. In a standard normal distribution, the value of mode is:

Equal to zero
Less than zero
Greater than zero
Exactly one

19. In normal distribution:

Mean = Median = Mode
Mean < Median < Mode
Mean > Median > Mode
Mean ≠ Median ≠ Mode

20. In normal probability distribution for a continuous random variable, the value of a mean deviation is approximately equal to:

(2/3)
2/3 σ
(4/5)
4/5 σ

21. Pearson’s constants for a normal distribution with mean μ and variance σ2 are:

β1=0, β2=0, γ1=0, γ2=0
β1=0, β2=1, γ1=1, γ2=3
β1=0, β2=3, γ1=0, γ2=0
β1=3, β2=0, γ1=0, γ2=0

22. The area to the left of (μ+σ) for a normal distribution is approximately equal to:

0.16
0.34
0.5
0.84

23. The coefficient of skewness of a normal distribution is:

Positive
Negative
Zero
Three

24. The lower and upper quartiles for a standardized normal variate are respectively:

-0.6745σ and 0.6745σ
-0.6745 σ and 0.6745
0.7979σ and 0.7979σ
-0.7979 and 0.7979

25. The maximum ordinate of a normal curve is at:

X = μ
X = μ + σ
X = μ - 2σ
X = σ²

26. The mean and standard deviation of the standard normal distribution a respectively:

0 and 1
1 and 0
μ and σ²
π and e

27. The median of a normal distribution corresponds to a value of Z is:

1
0.5
-0.5

28. The normal curve is symmetrical and for symmetrical distribution, the values of all odd order moments about mean will always be:

1
0.5
0.25

29. The normal distribution is a proper probability distribution of a continuous random variable, the total area under the curve f(x) is:

Equal to one
Less than one
More than one
Between -1 and +1

30. The normal probability density function curve is symmetrical about the mean, μ, i.e. the area to the right of the mean is the same as the area to the left of the mean. This means that P(X<μ) =P(X>μ) is equal to:

1
0.5
0.25