12th Business Mathematics and Statistics - Book Back Answers - Chapter 6 - English Medium Guides

 

 

Plus Two / 12th Business Mathematics and Statistics - Book Back Answers - Chapter 6 - English Medium

Tamil Nadu Board 12th Standard Business Mathematics and Statistics - Chapter 6: Book Back Answers and Solutions

    This post covers the book back answers and solutions for Chapter 6 – Business Mathematics and Statistics from the Tamil Nadu State Board 12th Standard Business Mathematics and Statistics textbook. These detailed answers have been carefully prepared by our expert teachers at KalviTips.com.

    We have explained each answer in a simple, easy-to-understand format, highlighting important points step by step under the relevant subtopics. Students are advised to read and memorize these subtopics thoroughly. Once you understand the main concepts, you’ll be able to connect other related points with real-life examples and confidently present them in your tests and exams.

    By going through this material, you’ll gain a strong understanding of Business Mathematics and Statistics  Chapter 6 along with the corresponding book back questions and answers (PDF format).

Question Types Covered:

• 1 Mark Questions: Choose the correct answer, Fill in the blanks, Identify the correct statement, Match the following 
• 2 Mark Questions: Answer briefly 
• 3, 4, and 5 Mark Questions: Answer in detail

All answers are presented in a clear and student-friendly manner, focusing on key points to help you score full marks.

All the best, Class 12 students! Prepare well and aim for top scores. Thank you!

Chapter 6:

I. Multiple Choice Questions

1. Value which is obtained by multiplying possible values of random variable with
probability of occurrence and is equal to weighted average is called
(a) discrete value
(b) weighted value
(c) expected value
(d) cumulative value
Answer Key:

(c) expected value

   

2. Demand of products per day for three days are 21, 19, 22 units and their respective probabilities are 0. 29, 0. 40, 0..35. Pofit per unit is 0. 50 paisa then expected profits for three days are
(a) 21, 19, 22 
(b) 21.5, 19.5, 22.5
(c) 0.29, 0.40, 0.35 
(d) 3.045, 3.8, 3.85
Answer Key:

(d) 3.045, 3.8, 3.85

 
3. Probability which explains x is equal to or less than particular value is classified as
(a) discrete probability
(b) cumulative probability
(c) marginal probability
(d) continuous probability
Answer Key:

(b) cumulative probability

 

4. Given E(X) = 5 and E(Y) = -2, then E(X – Y) is
(a) 3 
(b) 5 
(c) 7
(d) –2
Answer Key: 

(c) 7

 

5. A variable that can assume any possible value between two points is called
(a) discrete random variable
(b) continuous random variable
(c) discrete sample space
(d) random variable
Answer Key:

(b) continuous random variable

  

6. A formula or equation used to represent the probability distribution of a continuous random variable is called
(a) probability distribution
(b) distribution function
(c) probability density function
(d) mathematical expectation
Answer Key: 

(c) probability density function

  

7. If X is a discrete random variable and p(x) is the probability of X , then the expected value of this random variable is equal to
(a) $\sum f\left(x\right)$

(b) $\mathbf{\sum }\mathbf{[}\mathit{x}\mathbf{+}\mathit{f}\mathbf{(}\mathit{x}\mathbf{\left)}\mathbf{\right]}$
(c) $\sum f(x)+x$
(d) $\sum xp(x)$$$
Answer Key:

(d) $\sum xp(x)$

$$

8. Which of the following is not possible in probability distribution?
(a)$\mathbf{\sum }\mathbf{p}\mathbf{\left(}\mathbf{x}\mathbf{\right)}\mathbf{\ge }\mathbf{0}$
(b)$\mathbf{\sum }$p(x)= 1
(c)$\mathbf{\sum }$x p(x)= 2
(d)p(x)= − 0.5
Answer Key:

(d)p(x)= − 0.5

  

9. If c is a constant, then E(c) is
(a) 0
(b) 1
(c) c f (c) 
(d) c
Answer Key:

(d) c

 

10. A discrete probability distribution may be represented by
(a) table
(b) graph
(c) mathematical equation
(d) all of these
Answer Key:

(d) all of these

  

11. A probability density function may be represented by
(a) table
(b) graph
(c) mathematical equation
(d) both (b) and (c)
Answer Key:

(d) both (b) and (c)

  

12. If c is a constant in a continuous probability distribution, then p(x = c) is always equal to
(a) zero 
(b) one
(c) negative 
(d) does not exist
Answer Key:

(a) zero

 

13. E[X- E(X)] is equal to
(a) E(X) 

(b) V(X)
(c) 0

(d) E(X)− X
Answer Key:

(c) 0

 

14. $\mathit{E}\mathbf{[}\mathit{X}\mathbf{-}\mathit{E}\mathbf{(}\mathit{X}\mathbf{)}{\mathbf{]}}^{\mathbf{2}}$  is
(a) E(X) 

(b) E(${\mathit{X}}^{\mathbf{2}}$ )
(c) V(X) 

(d) S.D(X)
Answer Key:

(c) V(X)

 

15. If the random variable takes negative values, then the negative values will have
(a) positive probabilities
(b) negative probabilities
(c) constant probabilities
(d) difficult to tell
Answer Key:

(a) positive probabilities

  

16. If we have f (x)=2x,0 ≤ x ≤1 , then f (x) is a
(a) probability distribution
(b) probability density function
(c) distribution function
(d) continuous random variable
Answer Key:

(b) probability density function

  

17.$\underset{\mathbf{-}\mathbf{\infty }}{\overset{\mathbf{\infty }}{\mathbf{\int }}}$ f (x)dx is always equal to
(a) zero

(b) one
(c) E(X) 

(d) f (x)+1

Answer Key:

(b) one

  

18. A listing of all the outcomes of an experiment and the probability associated with each outcome is called
(a) probability distribution
(b) probability density function
(c) attributes
(d) distribution function
Answer Key:

(a) probability distribution

  

19. Which one is not an example of random experiment?
(a) A coin is tossed and the outcome is either a head or a tail
(b) A six-sided die is rolled
(c) Some number of persons will be admitted to a hospital emergency room during any hour.
(d) All medical insurance claims received by a company in a given year. 
Answer Key:

(d) All medical insurance claims received by a company in a given year.

 

20. A set of numerical values assigned to a sample space is called
(a) random sample
(b) random variable
(c) random numbers
(d) random experiment
Answer Key:

(b) random variable

  

21. A variable which can assume finite or countably infinite number of values is known as
(a) continuous

(b) discrete
(c) qualitative 

(d) none of them
Answer Key:

(b) discrete  

22. The probability function of a random variable is defined as

X=x	-1	-2	0	1	2
P(x)	k	2k	3k	4k	5k

Then k is equal to
(a)  zero 

(b) $\frac{\mathbf{1}}{\mathbf{4}}$ 
(c) $\frac{\mathbf{1}}{\mathbf{15}}$ 
(d) one

Answer Key:

(c) $\frac{\mathbf{1}}{\mathbf{15}}$ 

  

23. If p(x)=$\frac{\mathbf{1}}{\mathbf{10}}$, x = 10, then E(X) is
(a) zero 

(b) $\frac{\mathbf{6}}{\mathbf{8}}$ 
(c) 1 

(d) –1 

Answer Key:

(c) 1

  

24. A discrete probability function p(x) is always
(a) non-negative 

(b) negative
(c) one 

(d) zero  

Answer Key:

(a) non-negative 

  

25. In a discrete probability distribution the sum of all the probabilities is always equal to
(a) zero
(b) one
(c) minimum
(d) maximum

Answer Key:

(b) one

  

26. An expected value of a random variable is
(a) variance
(b) standard deviation
(c) mean
(d) covariance

Answer Key:

(c) mean

  

27. A discrete probability function p(x) is always non-negative and always lies between
(a) 0 and ∞ 

(b) 0 and 1
(c) –1 and +1

(d) –∞ and +∞
Answer Key:

(b) 0 and 1

 

28. The probability density function p(x) cannot exceed
(a) zero

(b) one
(c) mean

(d) infinity

Answer Key:

(b) one

  

29. The height of persons in a country is a random variable of the type
(a) discrete random variable
(b) continuous random variable
(c) both (a) and (b)
(d) neither (a) nor (b) 

Answer Key: 

(b) continuous random variable

  

30. The distribution function F(x) is equal to
(a) P(X = x)
(b) P(X ≤ x)
(c) P(X ≥ x)
(d) all of these

Answer Key: 

(b) P(X ≤ x)

II. Short answer questions

12th BM

III. Long answer questions

12th BM