Probability Distributions

The post is about Probability distributions MCQs with Answers. There are 20 multiple-choice questions covering topics related to binomial, Poisson, exponential, normal, gamma, standard normal, hypergeometric, and bivariable distributions. Let us start with the quiz probability distributions MCQs with answers.

Probability Distributions MCQS with Answers

• The number of products manufactured in a factory in a day is 3500 and the probability that some pieces are defective is 0.55 then the mean of the binomial probability distribution is
• A bank received 2600 applications for a home mortgage. The probability of approval is 0.78 then the standard deviation of the binomial probability distribution is
• Consider probability distribution as standard normal, if the value of $\mu$ is 75, the value of $x$ is 120 with an unknown standard deviation of distribution then the value of z-statistic
• If the value of $x$ is less than $\mu$ of standard normal probability distribution then the
• Standard normal probability distribution has a mean equal to 40, whereas the value of random variable x is 80 and the z-statistic is equal to 1.8, the standard deviation of the standard normal probability distribution is
• In binomial distribution, the formula for calculating standard deviation is
• If the value of $p$ is smaller or lesser than 0.5 then binomial distribution is classified as
• The continuous Random variable $X$ has a gamma distribution with Parameters $\alpha$ and $\beta$. The special gamma distribution for which $\alpha = 1$ is called.
• The continuous random variable $X$ has a gamma distribution with parameters $\alpha$ and $\beta$. The special gamma distribution for which $\alpha=\frac{v}{2}$ and $\beta=2$ where $v$ is a +ve integer is called.
• For a normal distribution, the measure of kurtosis equals to
• A bivariate normal distribution has a number of parameters in it
• The moment generating function of Binomial distribution is
• If $Mean > Variance$ then the distribution is
• If $Mean = Variance$ the distribution is called
• The area under the normal curve with $\mu\pm 2\sigma$ is
• The maximum ordinate of the normal curve is at
• Which of the following is NOT an assumption of the Binomial distribution?
• The normal distribution will be less spread out when
• Let $X$ be a positive random variable and let a new random variable $Y$ be defined as $Y=log X$. If $Y$ has a normal distribution then $X$ is
• If in a Gamma density, $k=1$ the Gamma density becomes

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The post is about MCQs Probability Distributions. There are 20 multiple-choice questions covering the topics related to Chi-Square distribution, F-distribution, Binomial distribution, Student’s t distribution, and properties of distributions. Let us start with MCQs Probability Distributions.

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MCQs Probability Distributions Quiz

• A family of parametric distribution in which mean always greater than its variance is:
• The family of parametric distributions which has a mean always less than variance is:
• The family of parametric distributions for which moment generating function does not exist is:
• The distribution for which the mode does not exist is:
• The relation between the mean and variance of $\chi^2$ with $n$ degrees of freedom is
• The $F$-distribution curve in respect of tails is:
• If $X$ has a binomial distribution with parameter $p$ and $n$ then $\frac{X}{n}$ has the variance:
• The binomial distribution is symmetrical if $p=p=?$
• The shape of geometric distribution is
• If $X\sim N(\mu, \sigma^2)$ and $a$ and $b$ are real numbers, then mean of $(aX+b)$ is
• The distribution of sample correlation is
• Events having an equal chance of occurrence are called
• Student’s $t$-distribution curve is symmetrical about mean, it means that
• The distribution possessing the memoryless property is
• The chi-square distribution is used for the test of
• The probability of failure in binomial distribution is denoted by
• In binomial distribution, the formula for calculating the mean is  
• In binomial probability distribution, dependents of standard deviations must include
• The formula to calculate standardized normal random variables is
• The mean of a binomial probability distribution is 857.6 and the probability is 64% then the number of values of binomial distribution

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The post is about Probability Distribution Questions. There are 20 multiple-choice questions covering topics related to normal probability distribution, standard normal probability distribution, and its properties. Let us start with the Quiz Probability Distribution Questions.

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Probability Distribution Questions with Answers

• The area under the normal curve on either side of the mean is
• In the case of a symmetrical distribution
• The mean deviation of Normal Distribution is
• The Normal Distribution has parameters
• In Normal distribution, the parameters which control the flatness of the curve is
• We use normal distribution when $n$ is
• The median of the normal distribution corresponds to the value of $Z$ equal to
• The lower and upper quartiles of standard normal variate are respectively
• The shape of the normal curve can be related to
• The total Area under the normal curve is
• Which of the following parameters controls the relative flatness of a normal distribution
• In a normal distribution $E(X−\mu)^2$ is
• If $X\sim N(55,49)$ then $\sigma$
• The Normal Curve is asymptotic to the
• The shape of the normal curve depends upon
• If $X\sim N(16, 49)$, then mean is
• Normal Distribution is
• If $Y=5X + 10$ and $X$ is $N(10,25)$, then mean of $Y$ is
• Normal Distribution is
• The formula in which binomial distribution approaches normal probability distribution with the help of normal variable is written as

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The post is about Continuous Probability Distribution Quiz. There are 20 multiple-choice questions. The quiz covers topics related to the distribution function, area under the curve, density function, binomial, geometric, and poison probability discrete distribution. Let us start with MCQs Continuous Probability Distribution Quiz.

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MCQs Continuous Probability Distribution Quiz

• A discrete probability distribution may be represented by
• The total Area under the curve in the probability of density function is
• The distribution function $F(X)$ is represented by
• The probability function is always
• For distribution Function $F(X)$, $F(−\infty)=0$ and $F(\infty) = ?$
• For a probability density function (PDF), the probability of a single point is
• The probability distribution of a random variable is also known as
• A continuous probability distribution can be represented by
• A discrete probability distribution may be represented by
• The central limit theorem states that the sampling distribution of the mean approaches a ——— distribution as the sample size increase.
• The Poisson distribution can model which of the following kinds of data? Select all that apply.
• The binomial distribution models the probability of events with ——— possible outcomes.
• The Poisson distribution can model the probability that a certain number of events will occur during a specific time period.
• What probability distribution represents experiments with repeated trials that each have two possible outcomes: success or failure?
• At what sample size does the t-distribution become practically the same as the normal distribution?
• What shape is the graph of the t-distribution?
• If $X$ has a normal distribution with mean $\mu$ and variance $\sigma^2$, then $y=\frac{(X-\mu)^2}{\sigma^2}$
• The binomial distribution is skewed right when
• In what case would the Poisson distribution be a good approximation of the binomial distribution:
• The mode of the geometric distribution is:

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