MCQs Normal Probability Distribution

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Test your knowledge of MCQs Normal Probability Distribution with this 20-question MCQ quiz! Perfect for statisticians, data analysts, and scientists, this quiz covers key concepts like parameters, symmetry, standard deviation, quartiles, skewness, and more. Ideal for exam prep, job interviews, and competitive tests, these questions help reinforce your understanding of the normal distribution, its properties, and applications. Sharpen your skills and assess your expertise in one of the most fundamental topics in statistics! Let us start with the Online MCQs Normal Probability Distribution now.

Online MCQs Normal Probability Distribution with Answers

Online MCQs about Normal Probability Distribution with Answers

1. In a normal distribution, the lower and upper quartiles are equidistant from the mean and are at a distance of

 
 
 
 

2. If $X\sim N(\mu, \sigma^2)$, the standard normal variate is distributed as

 
 
 
 

3. The value of $\pi$ is approximately equal to

 
 
 
 

4. The shape of the normal curve depends upon the value of

 
 
 
 

5. The normal curve is symmetrical, and for a symmetrical distribution, the values of all odd-order moments about the mean will always be

 
 
 
 

6. In a normal curve, the highest point on the curve occurs at the mean $\mu$, which is also the

 
 
 
 

7. The value of $e$ is approximately equal to

 
 
 
 

8. The total area of the normal probability density function is equal to

 
 
 
 

9. In a standard normal distribution, the value of the mode is

 
 
 
 

10. In a normal probability distribution for a continuous random variable, the value of the mean deviation is approximately equal to

 
 
 
 

11. if $x\sim N(\mu, \sigma^2)$, the points of inflection of normal distribution are

 
 
 
 

12. The normal distribution is a proper probability of a continuous random variable; the total area under the curve $f(x)$ is

 
 
 
 

13. In the normal distribution

 
 
 
 

14. In a normal curve, the ordinate is highest at

 
 
 
 

15. In a normal probability distribution of a continuous random variable, the value of the standard deviation is

 
 
 
 

16. The parameters of the normal distribution are

 
 
 
 

17. Which of the following is true for the normal curve

 
 
 
 

18. In a normal distribution whose mean is 1 and standard deviation 0, the value 4 quartile deviation is approximately

 
 
 
 

19. The coefficient of skewness of a normal distribution is

 
 
 
 

20. The range of the normal distribution is

 
 
 
 


Online MCQs Normal Probability Distribution with Answers

  • The range of the normal distribution is
  • In the normal distribution
  • Which of the following is true for the normal curve
  • In a normal curve, the ordinate is highest at
  • The parameters of the normal distribution are
  • The shape of the normal curve depends upon the value of
  • The normal distribution is a proper probability of a continuous random variable; the total area under the curve $f(x)$ is
  • In a normal probability distribution of a continuous random variable, the value of the standard deviation is
  • In a normal curve, the highest point on the curve occurs at the mean $\mu$, which is also the
  • The normal curve is symmetrical, and for a symmetrical distribution, the values of all odd-order moments about the mean will always be
  • if $x\sim N(\mu, \sigma^2)$, the points of inflection of normal distribution are
  • In a normal probability distribution for a continuous random variable, the value of the mean deviation is approximately equal to
  • In a normal distribution whose mean is 1 and standard deviation 0, the value 4 quartile deviation is approximately
  • In a normal distribution, the lower and upper quartiles are equidistant from the mean and are at a distance of
  • The value of $e$ is approximately equal to
  • The value of $\pi$ is approximately equal to
  • If $X\sim N(\mu, \sigma^2)$, the standard normal variate is distributed as
  • The coefficient of skewness of a normal distribution is
  • The total area of the normal probability density function is equal to
  • In a standard normal distribution, the value of the mode is

Exploratory Data Analysis in R

Factorial Experiment Design MCQs 17

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Test your knowledge of Factorial Experiment Design MCQs with this 20-question MCQ quiz! Perfect for students, statisticians, data analysts, and data scientists, this quiz covers key concepts like full factorial designs, interactions, orthogonality, contrasts, and fractional factorial experiments. Whether you’re preparing for exams, job interviews, or research, this quiz helps you master essential DOE (Design of Experiments) principles. Check your understanding of factors, levels, efficiency, and experimental regions with detailed answers provided. Sharpen your skills and boost your confidence in statistical experimental design today! Let us start with the Online Factorial Experiment Design MCQs now.

Please go to Factorial Experiment Design MCQs 17 to view the test
Online Factorial Experiment Design MCQs with Answers

Online Factorial Experiment Design MCQs with Answers

  • A factorial experiment is an experiment whose design consists of two or more factors, each with
  • Ronald Fisher and —————– are the pioneers of factorial design
  • A full factorial design is also called a fully
  • When Interaction is present, we should prefer
  • Factorial designs provide a chance to estimate the effect of a factor at ———— levels of the other factor
  • In the case of two factors, the relative efficiency of factorial design to one-factor-at-a-time experimental design is:
  • The factorial analysis requires that dependent variables be measured as
  • A factorial experiment requires that factors
  • In a $2^2$ design, the number of trials is equal to
  • Factorial experiments can involve factors with ————— levels
  • Orthogonality of a design can be checked by putting the levels of factors in
  • Factorial experiments can involve factors with —————– numbers of levels
  • The range of factor levels in which an experiment can be performed is commonly known as
  • In the first phase of the experiment, the stage that is completed is called
  • Typically region of experimentation is a cuboidal or a
  • A contrast may be used to know the magnitude or direction of —————.
  • Contrast can be used to compute
  • Average effect of $B$ for 3 replicates of experiment with factors $A$ and $B$ is computed by diving contrast to
  • The runs of two or more fractional factorial designs may be —————– to estimate the effects of vital interest
  • ————— factorial designs fill the gaps of the run size of the common factorial design.

Exploratory Data Analysis in R Language

Combining Events Using OR

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In probability and logic theory, combining events using OR (denoted as $\cup$) means considering situations where either one event occurs, or the other occurs, or both occur. This is known as the “inclusive OR.”

Given two events $A$ and $B$, one can define the event $A$ or $B$ to be the event that at least one of the events $A$ or $B$ occurs. The probability of the events $A$ or $B$ using the Addition Rule of probability can be computed easily. Learn the Basics of Probability.

Addition Rule of Probability (for Non-Mutually Exclusive Events)

If $A$ and $B$ are two events for an experiment, then
$$P(A\,\, or \,\,B) = P(A\cup B) = P(A) + P(B) – P(A\,\,and \,\, B)$$
This accounts for the overlap between events to avoid double-counting

Addition Rule Probability (for Mutually Exclusive Events)

Two events are called mutually exclusive events if both events cannot occur at the same time (cannot occur together). In this case, when the mutually exclusive events, $P(A\,\,\cap\,\,B)=0$, so the addition rule simplies to:
$$P(A\,\,or\,\,B) = P(A) + P(B)$$
This does not account for the overlap between events to avoid double-counting.

Combining Events using OR

Real Life Examples of Combining Events using OR

The following are a few real-life examples of Combining Events Using OR.

Weather Forecast Example

Suppose Event $A$ represents that it will rain tomorrow and Event $B$ that it will snow tomorrow. One can compute the probability that it will rain OR snow tomorrow. This means that at least one of them happens (it could be rain, snow, or both).
Suppose that the chance of rain tomorrow = $P(A)$ = 30% = 0.3. Supose that the probability of snow tomorrow = $P(B)$ = 20% = 0.2. Suppose the chances of both rain and snow are $P(A \cap B)$ = 5% = 0.5.
Therefore,
\begin{align*}
P(A \cup B) &= P(A) + P(B) – P(A \cup B) \\
& = 0.3 + 0.2 – 0.05 = 0.45
\end{align*}
There is a 45% chance that it will rain or snow tomorrow.

Job Requirements

Suppose Event $A$ represents that applicants must have a Bachelor’s degree, and Event $B$ represents that applicants must have 3 years of experience. One can compute the probability (or count) that the applicant must have a bachelor’s degree OR 3 years of experience to apply. The applicant will qualify if he/she have either one or both experiences.
Suppose there are 100 applicants for a certain job. For Event $A$, there are 40 applicants who have a Bachelor’s degree, and Event $B$ represents that there are 30 applicants who have more than 5 years of experience. Similarly, 10 applicants have both a Bachelor’s degree and have more than 3 years of experience. The number of qualifying applicants will be

\begin{align*}
A \cup B &= A + B – A \cap B \\
& = 40 + 30 – 10 = 60
\end{align*}
Therefore, 60 applicants meet at least one requirement (degree OR experience).

Restaurant Menu Choices

Consider Event $A$ represents the meal comes with fries, and Event $B$ represents the meal comes with a salad. One can compute if a customer can pick one, or sometimes both, if allowed. For illustrative purposes, suppose a Fast-Food Chain tracks 1000 orders. The Event $A$ represents 400 customers who choose fries, and Event $B$ represents 300 customers who choose a salad. Similarly, there are 100 customers who both choose fries and salad. The number of customers’ choices for both fries and salad will be

\begin{align*}
A \cup B &= A + B – A\cap B\\
&= 400 + 300 – 100 = 600
\end{align*}
600 customers ordered fries OR salad (or both).

Discount Offers

Let Event $A$ represent the use of a promo code for 10% off, Event $B$ represents a Student ID for 15% off. One uses a promo code or a Student ID to get a discount. Suppose a store offers two discount options to 200 customers. Event $A$ represents 65% of customers who used a coupon, Event $B$ represents that 13% customers showed their Student ID. 7% customers have used both the coupon and the Student ID. The probability that at least one discount is used will be

\begin{align*}
P(A \cup B) &= P(A) + P(B) – P(A \cap B)\\
& = 0.65 + 0.13 – 0.07 = 0.71
\end{align*}
71% of the customers have used at least one discount.

Security System Access

Suppose a building logs 500 entry attempts. Out of 500, 300 entries used a keycard, 200 used a PIN code, and 50 used both methods. What is the probability that both entry attempts are made?
\begin{align*}
P(A\cap B) &= P(A) + P(B) – P(A \cap B)\\
& = \frac{300}{500} + \frac{200}{500} – \frac{50}{500} = 0.6 + 0.4 – 0.1 = 0.9
\end{align*}
There are 90% ($500\times 0.9=450$) entries that used a keycard OR a PIN.

General Knowledge Quizzes

FAQs about Combining Events

  • What is meant by Combining Events?
  • What symbol is used to combine two or more events?
  • What rule of probability is used to combine events?
  • Give some real-life examples of Combining Events using OR.
  • What are mutually and Non-Mutually Exclusive Events?