Normal Distribution MCQ Questions and Answers for Practice

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

1. Zero
2. Less than zero
3. Greater than zero
4. None of the above

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

1. More than 0.5
2. Less than 0.5
3. Equal to 0.5
4. 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:

1. 0.8413
2. 0.3413
3. 0.1587
4. 0.5

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

1. ±σ
2. ±μ
3. σ ± μ
4. μ ± σ

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

1. N(1,0)
2. N(0,1)
3. N(μ,0)
4. N(0,σ²)

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

1. σ²
2. σ
3. 3σ⁴
4. β₁

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

1. Variance
2. Standard deviation
3. Quartile deviation
4. Mean deviation

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

1. 100
2. 64
3. 8
4. 100 - 64 = 36

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

1. Zero
2. One
3. Infinity
4. Hundred percent

10. If Z~N, then μ₄ is equal to:

1. 1
2. 3
3. σ⁴

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

1. 50% area
2. 68.27% area
3. 95.45% area
4. 99.73% area

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

1. Median and mode
2. Geometric mean and harmonic mean
3. Lower and upper quartiles
4. Variance and standard deviation

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

1. Mean
2. Variance
3. Standard deviation
4. Q1

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

1. (4/5)
2. 4/5 σ
3. 2/3 σ
4. (2/3)

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

1. 0.7979
2. 0.7979 σ
3. 0.6745
4. 0.6745 σ