MTH302 Lectures 41-45

MCQs on Normal Distribution

Q1. What does the standard normal distribution represent?

1. A normal distribution with mean = 0 and variance = 1
2. A normal distribution with mean = 1 and variance = 0
3. A normal distribution with mean = 1 and variance = 1
4. A distribution with no variance

Answer: A) A normal distribution with mean = 0 and variance = 1

Q2. What shape does the curve of a normal distribution take?

1. Uniform
2. Bell-shaped
3. Skewed
4. Linear

Answer: B) Bell-shaped

Q3. In a normal distribution, what is the total area under the curve?

1. 0.5
2. 1
3. Infinity
4. 100

Answer: B) 1

Q4. If X ∼ N(45,0.000625), what is the standard deviation (σ)?

1. 45
2. 0.025
3. 0.000625
4. D) 0.1

Answer: B) 0.025

Q5. What transformation converts a normal random variable X ∼ N(μ,σ2) to the standard normal distribution?

1. Z = Xσ−μ
2. Z = X + μ
3. Z = μ × X
4. Z = X2

Answer: A) Z = Xσ−μ

Q6. What is the probability of Z lying between 0 and 1.9 in the standard normal distribution?

1. 0.4713
2. 0.5
3. 0.9772
4. 0.3413

Answer: A) 0.4713

Q7. Which of the following is a property of the standard normal distribution?

1. Skewed to the left
2. Symmetrical about the mean
3. Area greater than 1
4. Discrete values

Answer: B) Symmetrical about the mean

Q8. For Z > 2, what is the probability?

1. 0.0228
2. 0.4772
3. 0.9772
4. 0.5

Answer: A) 0.0228

Q9. What is the probability that Z < 1.96 in the standard normal distribution?

1. 0.5
2. 0.975
3. 0.025
4. 0.4772

Answer: B) 0.975

Q10. In a standard normal table, the value 1.96 corresponds to which confidence interval?

1. 90%
2. 95%
3. 99%
4. 50%

Answer: B) 95%

Q11. The Z-score is used to...

1. Convert any normal distribution to a standard normal distribution
2. Determine the mode of the distribution
3. Calculate variance directly
4. Find discrete probabilities

Answer: A) Convert any normal distribution to a standard normal distribution

Q12. What is the formula for the probability density function of a normal distribution?

e−(x2−σμ2)2 A) y = B) y = ex−μ C) y = x2 + μ D) y = x1

Answer: A

Q13. What is the area under the curve for Z > 3?

1. Approximately 0.0013
2. 0.5
3. 0.02
4. 0.9772

Answer: A) Approximately 0.0013

Q14. What is the significance of symmetry in the standard normal curve?

1. All probabilities are equal
2. Areas on both sides of the mean are identical
3. Only positive values are allowed
4. Negative values are ignored

Answer: B) Areas on both sides of the mean are identical

Q15. If X ∼ N(50,16), the standard deviation (σ) is...

1. 16
2. 50
3. 4
4. 2

Answer: C) 4

Q16. The 99% confidence interval for Z is approximately...

1. ±1.96
2. ±2.58
3. ±3.00
4. ±1.64

Answer: B) ±2.58

Q17. If P(Z > 1.5) = 0.0668, what is P(Z < −1.5)?

1. 0.0668
2. 0.5
3. 0.4332
4. 0.9332

Answer: A) 0.0668

Q18. What is the cumulative probability for Z = 0?

1. 0
2. 0.5
3. 1
4. Undefined

Answer: B) 0.5

Q19. What is the probability P(−2 < Z < 2)?

1. 0.4772
2. 0.8185
3. 0.95
4. 0.3413

Answer: C) 0.95

Q20. What does a Z-score of 2 signify?

1. The value is 2 standard deviations above the mean
2. The value is 2 units above the mean