Probability Distributions

This Quiz contains the MCQs Probability Distributions Quiz. It covers events, experiments, mutually exclusive events, collectively exhaustive events, sure events, impossible events, addition and multiplication laws of probability, concepts related to discrete and continuous random variables, probability distribution and probability density functions, characteristics and properties of probability distributions, discrete probability distribution, and continuous probability distributions, etc.

Online MCQs about Probability Distributions with Answers

1. The mean deviation of a normal distribution is

 $\frac{5}4}\sigma$

 $\frac{3}{4}\sigma%

 $\frac{2}{5}\sigma$

 $\frac{4}{5}\sigma$

2. When can we use a normal distribution to approximate a binomial distribution?

 When both $np$ and $nq$ are greater than or equal to 5

 When $nq$ is greater than or equal to 5

 $When $np$ is greater than or equal to 5

 When $n$ is greater than 30

3. Which of the distributions has a larger variance than its mean

 Negative binomial

 Hypergeometric

 Poisson

 Binomial

4. The normal distribution is also classified as

 Weighted average distribution

 Bernoulli’s distribution

 Gaussian distribution

 Poisson distribution

5. In binomial probability distribution, the formula for calculating standard deviation is

 Square root of $np$

 Square root of $npq$

 Square root of $p$

 Square root of $pq$

6. For Beta distribution of 2nd kind, the range of $X$ is

 $X \in (0, 1)$

 $X\in (0, \infty)$

 $X \in (1, 0)$

 $X \in (-\infty, \infty)$

7. An oil company conducts a geological study that indicates that an exploratory oil well should have a 20% chance of striking oil. The company is interested in finding the probability that the first strike comes on the third well drilled. Which distribution distribution will be used?

 Geometric distribution

 Bernoulli distribution

 Negative binomial distribution

 Binomial distribution

8. A random variable $X$ has a binomial distribution with $n=9$, the variance of $X$ is

 $\sqrt{3}pq$

 $3pq$

 $3\sqrt{pq}$

 $\sqrt{3pq}$

9. In binomial probability distributions, the dependents of standard deviations must include

 Probability of $p$

 Probability of $q$

 Number of trials

 All of these options

10. The parameters of hypergeometric distributions are Note that $N$ is the population size, $n$ is the sample size, $p$ is the probability of successes, $K$ is a number of successes stated in the population, $k$ is the number of observed successes.

 $n$ and $k$

 $N, n,$ and $p$

 $N, K$, and $n$

 $n$ and $p$

11. If $X$ follows Geometric distribution with parameter $p$ (probability of success) then the Mean of $X$ is

 $p^2$

 $np$

 $\frac{1}{p}$

 $p$

12. In normal distribution, the proportion of observations that lies between 1 standard deviation of the mean is closest to

 0.99

 0.68

 0.95

 0.5

13. An oil company conducts a geological study that indicates that an exploratory oil well should have a 0.25 probability of striking oil. The company is interested in finding the probability that the 3rd strike comes on the 6th well drilled. Which distribution will be used?

 Binomial distribution

 Bernoulli distribution

 Geometric distribution

 Negative binomial distribution

14. For beta distribution of 1st kind, the range of $X$ is

 $X \in (0, 1)$

 $X \in (0, \infty)$

 $X \in (-\infty, \infty)$

 $X\in(1, 0)$

15. In any normal distribution, the proportion of observations that are outside $\pm$ standard deviation of the mean is closest to

 0.05

 0.95

 0.32

 0.68

16. Themean of the Poisson distribution is 9 then its standard deviation is

 36

 64

 3

 81

17. The Chi-Square distribution is a special case of

 Normal distribution

 Gamma distribution

 Exponential distribution

 Beta distribution

18. The distribution of the square of the standard normal random variable will be

 $F$

 $\chi^2$

 Standard Normal

 Normal

19. The formula of the mean of uniform or rectangular distribution is as

 $\frac{4(b+a)}{2b}$

 $\frac{(b-2a)}{4}$

 $\frac{(b+a)}{2}$

 $\frac{(2a+2b)}{2a}$

20. If $N$ is the population size, $n$ is the sample size, $p$ is the probability of success, $K$ is the number of successes stated in the population, and $k$ is the number of observed successes, then the parameters of the binomial distribution are

 $N, K$, and $n$

 $n$ and $p$

 $n$ and $k$

 $N, n$, and $p$

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Probability distributions are the foundation for various statistical tests like hypothesis testing. By comparing observed data to a theoretical distribution (the null hypothesis), we can assess the likelihood that the data arose by chance.

Probability distributions are crucial tools in data analysis. They help identify patterns, outliers, and relationships between variables. Furthermore, many statistical models depend on specific probability distributions to function accurately.

Online MCQs Probability Distributions Quiz

• In binomial probability distributions, the dependents of standard deviations must include
• In binomial probability distribution, the formula for calculating standard deviation is
• The formula of the mean of uniform or rectangular distribution is as
• The normal distribution is also classified as
• The mean deviation of a normal distribution is
• The Chi-Square distribution is a special case of
• Which of the distributions has a larger variance than its mean
• For Beta distribution of 2nd kind, the range of $X$ is
• The mean of the Poisson distribution is 9 then its standard deviation is
• In normal distribution, the proportion of observations that lies between 1 standard deviation of the mean is closest to
• For beta distribution of 1st kind, the range of $X$ is
• The parameters of hypergeometric distributions are Note that $N$ is the population size, $n$ is the sample size, $p$ is the probability of successes, $K$ is a number of successes stated in the population, $k$ is the number of observed successes.
• If $N$ is the population size, $n$ is the sample size, $p$ is the probability of success, $K$ is the number of successes stated in the population, and $k$ is the number of observed successes, then the parameters of the binomial distribution are
• An oil company conducts a geological study that indicates that an exploratory oil well should have a 0.25 probability of striking oil. The company is interested in finding the probability that the 3rd strike comes on the 6th well drilled. Which distribution will be used?
• If $X$ follows Geometric distribution with parameter $p$ (probability of success) then the Mean of $X$ is
• The distribution of the square of the standard normal random variable will be
• A random variable $X$ has a binomial distribution with $n=9$, the variance of $X$ is
• In any normal distribution, the proportion of observations that are outside $\pm$ standard deviation of the mean is closest to
• When can we use a normal distribution to approximate a binomial distribution?
• An oil company conducts a geological study that indicates that an exploratory oil well should have a 20% chance of striking oil. The company is interested in finding the probability that the first strike comes on the third well drilled. Which distribution distribution will be used?

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