12th Business Mathematics and Statistics - Book Back Answers - Chapter 7 - English Medium Guides

 

 

Plus Two / 12th Business Mathematics and Statistics - Book Back Answers - Chapter 7 - English Medium

Tamil Nadu Board 12th Standard Business Mathematics and Statistics - Chapter 7: Book Back Answers and Solutions

    This post covers the book back answers and solutions for Chapter 7 – 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 7 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 7:

I. Multiple Choice Questions

1. Normal distribution was invented by
(a) Laplace 

(b) De-Moivre
(c) Gauss 

(d) all the above
Answer Key:

(b) De-Moivre 

2. If X ~N(9,81) the standard normal variate Z will be
(a) Z=$\frac{\mathit{X}\mathbf{-}\mathbf{81}}{\mathbf{9}}$
(b) Z =$\frac{\mathit{X}\mathbf{-}\mathbf{9}}{\mathbf{81}}$
(c) Z =$\frac{\mathit{X}\mathbf{-}\mathbf{9}}{\mathbf{9}}$
(d) Z =$\frac{\mathbf{9}\mathbf{-}\mathit{X}}{\mathbf{9}}$
Answer Key:
(c) Z =$\frac{\mathit{X}\mathbf{-}\mathbf{9}}{\mathbf{9}}$

$\frac{\mathbf{ }}{}$
3. If Z is a standard normal variate, the proportion of items lying between Z = –0.5 and Z = –3.0 is
(a) 0.4987 

(b) 0.1915
(c) 0.3072 

(d) 0.3098
Answer Key:
(c) 0.3072

 
4. If X ~N(μ, ${\mathit{\sigma }}^{\mathbf{2}}$), the maximum probability at the point of inflexion of normal distribution is
(a)$<math\; xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi\; mathvariant="bold-italic">e</mi><mfrac><mn\; mathvariant="bold">1</mn><mn\; mathvariant="bold">2</mn></mfrac></msup></math>$

(b)⁽$<math\; xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfrac><mn\; mathvariant="bold">-1</mn><mn\; mathvariant="bold">2</mn></mfrac></msup></math>$⁾$<math\; xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi\; mathvariant="bold-italic"></mi></msup></math>$
(c)$e$⁽$<math\; xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfrac><mn\; mathvariant="bold">-1</mn><mn\; mathvariant="bold">2</mn></mfrac></msup></math>$⁾
(d)$<math\; xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi\; mathvariant="bold-italic"></mi></msup></math>$
Answer Key:

(c)$e$⁽$<math\; xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfrac><mn\; mathvariant="bold">-1</mn><mn\; mathvariant="bold">2</mn></mfrac></msup></math>$⁾

  
5. In a parametric distribution the mean is equal to variance is
(a) binomial 

(b) normal
(c) poisson 

(d) all the above
Answer Key:
(c) poisson 

 
6. In turning out certain toys in a manufacturing company, the average number of defectives is 1%. The probability that the sample of 100 toys there will be 3 defectives is
(a) 0.0613 

(b) 0.613
(c) 0.00613 

(d) 0.3913
Answer Key:
(a) 0.0613

 
7. The parameters of the normal distribution f(x)= $\frac{{{\mathit{e}}^{\mathbf{-}\mathbf{(}\mathit{x}\mathbf{-}\mathbf{10}\mathbf{)}}}^{\mathbf{2}}}{\mathbf{72}}$ -∞< x < ∞
(a) (10,6) 

(b) (10,36)
(c) (6,10) 

(d) (36,10)
Answer Key:
(b) (10,36)

 
8. A manufacturer produces switches and experiences that 2 per cent switches are defective. The probability that in a box of 50 switches, there are atmost two defective is :
(a) 2.5 ${\mathit{e}}^{\mathbf{-}\mathbf{1}}$
(b) ${\mathit{e}}^{\mathbf{-}\mathbf{1}}$
(c) 2 ${\mathit{e}}^{\mathbf{-}\mathbf{1}}$
(d) none of the above
Answer Key:
(a) 2.5 ${\mathit{e}}^{\mathbf{-}\mathbf{1}}$

${\mathbf{ }}^{}$
9. An experiment succeeds twice as often as it fails. The chance that in the next six trials, there shall be at least four successes is
(a) 240/729 

(b) 489/729
(c) 496/729 

(d) 251/729
Answer Key:
(c) 496/729 

 
10. If for a binomial distribution B(n,p) mean = 4 and variance = 4/3, the probability, P(X ≥ 5) is equal to
(a) (2/3)⁶ 

(b) (2/3)⁵(1/3)
(c) (1/3)⁶

(d) 4(2/3)⁶
Answer Key:

 (d) 4(2/3)⁶

 
11. The average percentage of failure in a certain examination is 40. The probability that out of a group of 6 candidates atleast 4 passed in the examination are
(a) 0.5443 

( b) 0.4543
(c) 0.5543 

(d) 0.4573
Answer Key:
(a) 0.5443 

 
12. Forty percent of the passengers who fly on a certain route do not check in any luggage. The  planes on this route seat 15  passengers. For a full flight, what is the mean of the number of passengers who do not check in any luggage?
(a) 6.00 

(b) 6.45
(c) 7.20 

(d) 7.50
Answer Key:
(a) 6.00 

 
13. Which of the following statements is/are true regarding the normal distribution curve?
(a) it is symmetrical and bell shaped curve
(b) it is asymptotic in that each end approaches the horizontal axis but never reaches it
(c) its mean, median and mode are located at the same point
(d) all of the above statements are true.
Answer Key:
(d) all of the above statements are true.

 
14. Which of the following cannot generate a Poisson distribution?
(a) The number of telephone calls received in a ten-minute interval
(b) The number of customers arriving at a petrol station
(c) The number of bacteria found in a cubic feet of soil
(d) The number of misprints per page
Answer Key:
(b) The number of customers arriving at a petrol station

 
15. The random variable X is normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is between 72 and 84?
(a) 0.683 

(b) 0.954
(c) 0.271 

(d) 0.340
Answer Key:
(d) 0.340

 
16. The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of `1,80,000 and a standard  deviation of `10,000. What is the probability that a randomly selected newly qualified CA will earn between `1,65,000 and `1,75,000 per annum?
(a) 0.819 

(b) 0.242
(c) 0.286 

(d) 0.533
Answer Key:
(b) 0.242

 
17. In a large statistics class the heights of the students are normally distributed with a mean of 172cm and a variance of 25cm. What proportion of students are between 165cm and 181cm in height?
(a) 0.954 

(b) 0.601
(c) 0.718 

(d) 0.883
Answer Key:
(d) 0.883

 
18. A statistical analysis of long-distance telephone calls indicates that the length of these calls is normally distributed with a mean of 240 seconds and a standard deviation of 40 seconds. What proportion of calls lasts less than 180 seconds?
(a) 0.214 

(b) 0.094
(c) 0933 

(d) 0.067
Answer Key:
(d) 0.067

 
19. Cape town is estimated to have 21% of homes whose owners subscribe to the satelite service, DSTV. If a random sample of your home in taken, what is the probability that all four home subscribe to DSTV?
(a) 0.2100 

(b) 0.5000
(c) 0.8791 

(d) 0.0019
Answer Key:
(d) 0.0019

 
20. Using the standard normal table, the sum of the probabilities to the right of z = 2.18 and to the left of z = –1.75 is
(a) 0.4854 

(b) 0.4599
(c) 0.0146 

(d) 0.0547
Answer Key:

(d) 0.0547

  
21. The time until first failure of a brand of inkjet printers is normally distributed with a mean of 1,500 hours and a standard deviation of 200 hours. What proportion of printers fails before 1,000 hours?
(a) 0.0062 

(b) 0.0668
(c) 0.8413 

(d) 0.0228
Answer Key:
(a) 0.0062 

 
22. The weights of newborn human babies are normally distributed with a mean of 3.2kg and a standard deviation of 1.1kg. What is the probability that a randomly selected newborn baby weighs less than 2.0kg?
(a) 0.138 

(b) 0.428
(c) 0.766 

(d) 0.262
Answer Key:
(a) 0.138 

 
23. Monthly expenditure on their credit cards, by credit card holders from a certain bank, follows a normal distribution with a mean of `1,295.00 and a standard deviation of `750.00. What proportion of credit card holders spend more than `1,500.00 on their credit cards per month?
(a) 0.487 

(b) 0.392
(c) 0.500 

(d) 0.791
Answer Key:
(b) 0.392

 
24. Let z be a standard normal variable. If the area to the right of z is 0.8413, then the value of z must be:
(a) 1.00 

(b) –1.00
(c) 0.00 

(d) –0.41
Answer Key:
(b) –1.00

 
25. If the area to the left of a value of z (z has a standard normal distribution) is 0.0793, what is the value of z?
(a) –1.41 

(b) 1.41
(c) –2.25 

(d) 2.25
Answer Key:
(a) –1.41

 
26. If P(Z > z) = 0.8508 what is the value of z (z has a standard normal distribution)?
(a) –0.48 

(b) 0.48
(c) –1.04 

(d) 1.04
Answer Key:

(c) –1.04

  
27. If P(Z > z) = 0.5832 what is the value of z (z has a standard normal distribution)?
(a) –0.48 

(b) 0.48
(c) 1.04 

(d) –0.21
Answer Key:
(d) –0.21

 
28. In a binomial distribution, the probability of success is twice as that of failure. Then out of 4 trials, the probability of no success is
(a) 16/81

(b) 1/16
(c) 2/27 

(d) 1/81
Answer Key:

(d) 1/81

 

II. Short answer questions

12th BM

III. Long answer questions

12th BM