Probability Distributions

Introduction to Probability Distributions, Discrete Probability, Continuous Probability, Distribution Functions, Density Functions, Real life Examples of Probability Distributions

Normal Probability Distribution MCQs 13

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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 Normal Probability Distribution MCQs with Answers

Online Multiple Choice Type Questions about Normal Probability Distribution with Answers

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

15. 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

 
 
 
 

16. 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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 


  • 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

Normal Distribution Quiz 12

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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
Please go to Normal Distribution Quiz 12 to view the test

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

R Language Frequently Asked Questions

Normal Probability Distribution Quiz 11

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Master the Normal Probability Distribution Quiz with this 20-MCQ Test! Test your knowledge of key concepts like symmetry, standard deviation, skewness, kurtosis, and more. Perfect for students, learners, data analysts, and professionals preparing for exams, job tests, and interviews. Includes detailed answers & explanations to boost your understanding of probability distributions. Let us start with the Online Normal Probability Distribution Quiz now.

Online Normal Probability Distribution Quiz with Answers
Please go to Normal Probability Distribution Quiz 11 to view the test

Online Normal Probability Distribution Quiz with Answers

  • The normal probability density function curve is symmetrical about the mean $\mu$, that is, the area to the right of the mean is the same as the area to the left of the mean. This means that $P(X<\mu)=P(X>\mu)$ is equal t:
  • The skewness and kurtosis of the normal distribution are, respectively
  • In a normal curve $\mu \pm 0.6745\sigma$ covers
  • The lower and upper quartiles for a standardized normal variate are, respectively
  • The maximum ordinate of a normal curve is at
  • The value of the standard deviation $\sigma$ of a normal distribution is always
  • If $X\sim N(100, 64)$ then standard deviation $\sigma$ is
  • If $Z\sim N(0, 1)$ the coefficient of variation is equal to
  • The points of inflection of the standard normal distribution lie at
  • If $Z\sim N(0, 1)$ then $\mu_4$ is equal to
  • The value of the second moment about the mean in a normal distribution is 5. The fourth moment about the mean in the distribution is
  • If $X$ is a normal random variable having mean $\mu$ then $E|X-\mu|$ is equal to
  • If $X$ is a normal random variable having mean $\mu$ then $E(X-\mu)^2$ is equal to
  • Which of the following is possible in a normal distribution?
  • The range of the standard normal distribution is
  • In the normal distribution, the value of the maximum ordinate is equal to
  • The value of the ordinate at points of infection of the normal curve is equal to
  • If $Z\sim N(0,1)$ then $\beta_2$ is equal to
  • Pearson’s constants for a normal distribution with mean $\mu$ and variance $\sigma^2$ are
  • The value of the maximum ordinate in the standard normal distribution is equal to

R Language Frequently Asked Questions