Muhammad Imdad Ullah

Test your understanding of Normal and Standard Normal distribution with these key MCQs. The Quiz Normal Probability Distribution MCQs covers probabilities, Z-scores, percentiles, transformations, and real-world applications. This Normal Probability Distribution MCQs Quiz is perfect for:

• Statistics students (GATE, UG/PG exams)
• Data analysts & scientists (interview prep)
• Competitive exams (IAS, ACT, GRE)
  Includes detailed solutions for concepts like empirical rule, quartiles, mean deviation, and CLT. Boost your stats skills now!

Online Normal Probability Distribution MCQs with Answers

Online Multiple Choice Type Questions about Normal Probability Distribution with Answers

1. If $Y=5x+10$ and $X$ is N(10, 25), then mean of $Y$ is

 60

 135

 70

 50

2. The probability $P(Z\le 1.96)$ is approximately

 0.025

 0.95

 0.05

 0.975

3. If $X \sim N(10, 4)$ and $Y\sim N(15, 9)$ are independent, what is the distribution of $X+Y$?

 $N(25, 13)$

 $N(25, 5)$

 $N(25, 6)$

 $N(25, 36)$

4. Given a random variable $X$ which is normally distributed with a mean and variance both equal to 100. The value of the mean deviation is approximately equal to

 8.5

 7

 8

 9

MD = $\sqrt{2}{\pi}\times \sigma$

5. If $X\sim N(\mu, \sigma^2)$ then $Z=\frac{X-\mu}{\sigma}$ follows

 $N(1, 0)$

 $N(\mu, \sigma^2)$

 Uniform distribution

 $N(0, 1)$

6. If $Z$ is a standard normal variate, then $P(-1.645 \le Z \le 1.645)$ is equal to

 0.95

 0.99

 0.90

 0.98

7. In a normal distribution mean is 100 and the standard deviation is 10. The values of points of infection are:

 80 and 120

 100 and 110

 90 and 110

 None of these

8. If $X$ is a normal variate with mean 20 and variance 1.6. The respective values of $\beta_1$ and $\beta_2$ are

 0.5 and 1

 0 and 3

 3 and 1

 3 and 3

9. If $X$ is a normal variate with mean 50 and standard deviation 3, the value of the quartile deviation is approximately equal to

 2.5

 1

 2

 1.5

10. If a normal distribution with $\mu=200$ have $P(X> 22.5)=0.1587$ then $P(X<175)$ equal to

 0.3413

 0.1587

 0.8413

 0.5000

11. If $Z$ is a standard normal variate, then $P(|Z| < 1.96)$ is equal to

 0.4750

 0.0250

 0.95

 0.9750

12. For a normal distribution with $\mu = 10, \sigma = 2$ the probability of a value greater than 10 is

 0.1915

 0.6915

 0.5000

 0.3085

13. If $X$ is a normal random variable with mean $\mu=50$ and standard deviation $\sigma = 7$, if $Y=x-7$ then standard deviation of $Y$ is

 0

 7

 49

 14

14. If $Z$ is a standard normal variate, then $P(-2.33\le Z \le 2.33)$ is equal to

 0.6827

 0.9545

 0.9802

 0.4901

15. If $X$ is $N(100, 5)$ the fourth central moment is

 65

 85

 75

 100

$\mu_4 = 3\sigma^4$

16. Given a normal distribution with $\mu=100$ and $\sigma^2=100$, the area to the left of 100 is

 Greater than 0.5

 Less than 0.5

 One

 Equal to 0.5

17. A normal distribution has the mean $\mu=200$. If 70% of the area under the curve lies to the left of 220, the area to the right of 220 is

 0.50

 0.20

 0.70

 0.30

18. A random variable has a normal distribution with the mean $\mu=400$. If 8% of the area under the curve lies to the left of 500, the area between 400 and 500 is

 0.3

 0.5

 0.2

 Zero

19. The 99th percentile of the standard normal distribution is closest to:

 3.00

 2.33

 1.96

 2.58

20. If $Z$ is a standard normal variate, then $P(-2.575\le Z \le 2.575)$ is equal to

 0.4951

 0.9951

 0.99

 0.4909

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• If $Z$ is a standard normal variate, then $P(-1.645 \le Z \le 1.645)$ is equal to
• If $Z$ is a standard normal variate, then $P(-2.33\le Z \le 2.33)$ is equal to
• If $Z$ is a standard normal variate, then $P(-2.575\le Z \le 2.575)$ is equal to
• If $Z$ is a standard normal variate, then $P(|Z| < 1.96)$ is equal to
• For a normal distribution with $\mu = 10, \sigma = 2$, the probability of a value greater than 10 is
• Given a random variable $X$ which is normally distributed with a mean and variance both equal to 100. The value of the mean deviation is approximately equal to
• If $X$ is a normal variate with mean 50 and standard deviation 3, the value of the quartile deviation is approximately equal to
• In a normal distribution mean is 100 and the standard deviation is 10. The values of points of infection are:
• If $X$ is a normal variate with mean 20 and variance 1.6. The respective values of $\beta_1$ and $\beta_2$ are
• If $X$ is $N(100, 5)$, the fourth central moment is
• A normal distribution has the mean $\mu=200$. If 70% of the area under the curve lies to the left of 220, the area to the right of 220 is
• Given a normal distribution with $\mu=100$ and $\sigma^2=100$, the area to the left of 100 is
• If a normal distribution with $\mu=200$ have $P(X> 22.5)=0.1587$ then $P(X<175)$ equal to
• A random variable has a normal distribution with the mean $\mu=400$. If 8% of the area under the curve lies to the left of 500, the area between 400 and 500 is
• If $Y=5x+10$ and $X$ is N(10, 25), then mean of $Y$ is
• If $X$ is a normal random variable with mean $\mu=50$ and standard deviation $\sigma = 7$, if $Y=x-7$ then standard deviation of $Y$ is
• If $X\sim N(\mu, \sigma^2)$ then $Z=\frac{X-\mu}{\sigma}$ follows
• The probability $P(Z\le 1.96)$ is approximately
• The 99th percentile of the standard normal distribution is closest to:
• If $X \sim N(10, 4)$ and $Y\sim N(15, 9)$ are independent, what is the distribution of $X+Y$?

The GLM Function in R Language

Test your understanding of the Normal Distribution Quiz with this 20-question MCQ Test! Perfect for statisticians, data analysts, and students preparing for exams or job interviews. Covers key concepts such as mean, variance, standard deviation, Z-scores, and probability under the normal distribution. Check your answers and sharpen your statistical skills today! Let us start with the Online Normal Distribution Quiz now.

Online Normal Distribution Quiz with Answers

• A random variable $X$ is normally distributed with $\mu=70$ and $\sigma^2=25$. The third moment about the arithmetic mean is
• For the standard normal distribution $P(Z > mean)$ is
• Given a standardized normal distribution (with a mean of zero and a standard deviation of one), $P(Z<variance)$ is equal to
• The area to the left of $(\mu + \sigma)$ for a normal distribution is approximately equal to
• The median of a normal distribution corresponds to a value of $Z$ is ———.
• The mean and standard deviation of the standard normal distribution are, respectively:
• In a standard normal distribution, the area to the left of $Z=1$ is
• The semi-interquartile range for a standard normal random variable $Z$ is
• If $X\sim N(\mu, \sigma^2)$ then $\mu_4$ is equal to
• If $X\sim N(\mu, \sigma^2)$ then $\beta_2$ is equal to
• $P(\mu – \sigma < X <\mu + \sigma)$ is equal to
• In a normal curve $\mu \pm 2\sigma$ covers
• In $X$ is $N(\mu, \sigma^2)$, the percentage of the area contained within the limits $\mu\pm 3\sigma$
• Most of the area under the normal curve with parameter $\mu$ and $\sigma$ lies between
• The probability density function of the standard normal distribution is
• The equation of the normal frequency distribution is
• If $X$ is $N(\mu, \sigma^2)$ and if $Y=a+bX$ then mean and variance of $Y$ are, respectively:
• For a normal distribution with mean $\mu$ and standard deviation $\sigma$
• The normal probability distribution with mean $np$ and variance $npq$ may used to approximate the binomial distribution if $n\ge 50$ and both $np$ and $nq$ are
• In a normal distribution, $Q_1=20$ and $Q_3=40$ then the mean is equal to

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