MTH302- Business Mathematics & Statistics Complete Solved Final Term Paper

FINALTERM  EXAMINATION

Fall 2008

MTH302- Business Mathematics & Statistics (Session - 1)

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Question No: 1    ( Marks: 1 )    - Please choose one

The c2 distribution is  ---------------

       ► Positively skewed

       ► Negatively skewed

       ► Symmetrical

       ► None of these

   

Question No: 2    ( Marks: 1 )    - Please choose one

 In the regression line Y = a + bX., a represents

►Intercept of the line

►Slope of the line

►Slope of the curve

►None of the above

   

Question No: 3    ( Marks: 1 )    - Please choose one

In the formula, ,  e is a constant whose value is ……………

       ► 2.71828

       ► 3.14157

       ► 22 / 7

       ► 9.325

   

Question No: 4    ( Marks: 1 )    - Please choose one

 Which distribution is most commonly used for the continuous data?

       ► Normal Distribution

       ► Binomial Distribution

       ► Poisson Distribution

       ► Negative Binomial Distribution

   

Question No: 5    ( Marks: 1 )    - Please choose one

 For any event if the probability of success is x,  then the probability of  failure is

       ► also x

       ► 1 + x

       ► 1 – x 

       ► x - 1

   

Question No: 6    ( Marks: 1 )    - Please choose one

  The standard deviation of any sampling distribution is called

       ► sampling error

       ► type –I error 

       ► standard error

       ► non sampling error

   

Question No: 7    ( Marks: 1 )    - Please choose one

 For graphing univariate data we use

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       ► Pie charts,Bar charts .

       ► Pareto diagrams.

       ► Side by side chart .

       ► Both (1) & (2)

   

Question No: 8    ( Marks: 1 )    - Please choose one

 Interest paid (earned) on only the original principal borrowed (lent) is often referred to as

       ► simple interest

       ► present value

       ► future value

       ► compound interest

   

Question No: 9    ( Marks: 1 )    - Please choose one

 The sales of a company increases from Rs.100,000 last month to Rs.120,000 this month. The percentage change in profit for the month?

       ► 20%

       ► 40%

       ► 10%

       ► 60%

   

Question No: 10    ( Marks: 1 )    - Please choose one

 Amount of discount is obtained as

       ► Percentage of Discount x List Price

       ► Percentage of Discount / List Price

       ► Percentage of Discount - List Price

       ► None of these

   

Question No: 11    ( Marks: 1 )    - Please choose one

 If a and b are any two integers such that a<b then a-b is

       ► positive

       ► negative

       ► canot be told

       ► zero

   

Question No: 12    ( Marks: 1 )    - Please choose one

 If the salary of an employee is 10,000 and his allowances are 5,000 then what is the taxable income of the employee?

       ► 5,000

       ► 10,000

       ► Zero    

       ► 15,000

   

Question No: 13    ( Marks: 1 )    - Please choose one

 Compound interest is always:

       ► Higher than simple interest

       ► Smaller than simple interest

       ► Less than annuity

       ► Equals to simple interest

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Question No: 14    ( Marks: 1 )    - Please choose one

 The RSQ of any data is

       ► Square root of correlation coefficient.

       ► Square of correlation coefficient.

       ► Correlation coefficient.

       ► Slope of the data.

   

Question No: 15    ( Marks: 1 )    - Please choose one

 12% of the electric bulbs manufactured by a company are defective. What is the probability that a bulb selected will not be defective?

       ► 90 %

       ► 88 %

       ► 80 %

       ► 85 %

   

Question No: 16    ( Marks: 1 )    - Please choose one

 If there is a indirect relationship between rainfall & yield of crops then

       ► Yield is higher if rainfall is less

       ► Yield is lower if rainfall is less

       ► Yield is higher if rainfall is higher

       ► Yield is higher if rainfall is nothing

   

Question No: 17    ( Marks: 1 )    - Please choose one

 If the estimating equation is Y = a – b X, which of the following is true

       ► The y intercept is b

       ► Slope of line is positive

       ► There is inverse relationship

       ► There is direct relationship

   

Question No: 18    ( Marks: 1 )    - Please choose one

 How many ways can 4 prizes be given away to 3 boys, if each boy is eligible for all the prizes?

       ► 256

       ► 12

       ► 81

       ► None of these

   

Question No: 19    ( Marks: 1 )    - Please choose one

 How many ways can 10 letters be posted in 5 post boxes, if each of the post boxes can take more than 10 letters?

       ► 5^10

       ► 10^5

       ► 10P5

       ► 10C5

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Question No: 20    ( Marks: 1 )    - Please choose one

 Equation of line having slope 0 and passing through the point A (0, 0) is

       ► X =0

       ► Y= X

       ► Y=0

       ► X-1= 0

   

Question No: 21    ( Marks: 2 )

 Define the Null Hypothesis.

ANS: Null hypothesis is a scenario which explain a given set of data. It is tested to determine whether data provides sufficient reasons to pursue some alternative hypothesis.

It is a hypothesis that states there is no difference between 2 or more sets of data.

   

Question No: 22    ( Marks: 2 )

 A coin can be tossed in 3 ways. A die can be thrown in 6 ways. A coin and a die together can be thrown in …3 X 6 = 18……….ways.

   

Question No: 23    ( Marks: 2 )

 Find harmonic mean (HM) of 10,12,14,17.

ANS: Harmonic mean,HM = n/(1/x1 + 1/x2 + 1/x3 + 1/x4 +…… +1/xn)

                                         

N= 4

X₁ = 10

X₂ = 12

X₃ = 14

X₄ = 17

1/x1 + 1/x2 + 1/x3 + 1/x4 = 1/10 + 1/12+ 1/14+ 1/17 = 0.2385

Harmonic mean = 4/0.2385= 16.77

   

Question No: 24    ( Marks: 3 )

Find proportion of bags which have weight in excess of 505 g.

          Mean = 500.

          StDev = 2.5 g

          (For z=2.00 probability is 0.4772)

    

Question No: 25    ( Marks: 3 )

 Given for a frequency distribution  mode = 18, mean = 21.Calculate  median . Using these values comment on skewness of distribution.

ANS: We know that,

           Mean-mode= 3(mean- median)

           Median= (2*mean+mode)/3

  Since,

           Mean= 21

           Mode= 18

So,

           Median = (2*21+18)/3

                        = (42+18)/3 = 60/3 = 10

The distribution is Moderately skewed and unimodal distribution.

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Question No: 26    ( Marks: 3 )

 How many different ways can you select 2 letters from the set of letters: X, Y, and Z? (Hint: In this problem, order is NOT important; i.e., XY is considered the same selection as YX.)

ANS: Total number of letters = 3

          Letters taken at a time = 2

          Number of ways in which 2 letters can be selected out of 3 = ³C₂ = 3! / 2!(3-2)!

                                                                                                                   =3*2*1/ 2

                                                                                                                   = 3

   

Question No: 27    ( Marks: 5 )

 How many possible permutations can be formed from the word MATHEMATICS?

ANS:  Total number of alphabets in mathematics = 11

M = 2

A = 2

T = 2

H = 1

E = 1

I = 1

C = 1

S = 1

Permutations = 11! / 2! * 2! * 2! *1! * 1! * 1* 1! * 1!

                      = 11! / 8 = 4,989,600

   

Question No: 28    ( Marks: 5 )

 Find the standard deviation of 4, 9, 11, 12, 17, 5, 8, 12, 14

ANS: Standard deviation for sample = sqrt[sum(X- )²/n-1)

= mean = (4+9+11+12+17+5+8+12+14)/9 = 92/9 = 10.22

n= 9

so , n-1 =9-1 = 8

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X	X-	(X- )2
4	-6.22	38.69
9	-1.22	1.49
11	0.78	0.61
12	1.78	3.17
17	6.78	45.97
5	-5.22	27.25
8	-2.22	4.93
12	1.78	3.17
14	3.78	14.29

² = 139.57

Standard deviation = = 4.18

Question No: 29    ( Marks: 5 )

 In a normal distribution  what proportion of cases will fall between 20 and 35?

   

Question No: 30    ( Marks: 10 )

  Form a regression line from the data below.

Departments	X	Y
1	26	81
2	42	95
3	16	53
l4	55	43
5	92	18
6	28	63
7	13	60

    ANS: Slope ,b = [n*sum(X*Y) – sumX*sumY]/ [n*sumX²- (sumX)²]

              intercept, a = (sumY – b*sumX)/n

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             n= 7

Departments	X	Y	X2	X*Y
1	26	81	676	2106
2	42	95	1764	3990
3	16	53	256	848
4	55	43	3025	2365
5	92	18	8464	1656
6	28	63	784	1764
7	13	60	169	780

sumX =272

sumY= 413

sumX² = 15138

sumX*Y = 13509

slope, b = [7(13509)-272*413]/[7(15138)-(272)²]

                   = -17,773/31,982 = -0.55

intercept, a =  [413-(-0.55)272]/ 7 = 80.37

equation of regression line is given by,

  Y = a+ bx

  Y = 80.37 -0.55x

Question No: 31    ( Marks: 10 )

 The following data gives the height (in inches) of eleven 9-years old boys in a primary school.

57, 52, 51, 49, 55, 54, 50, 48, 53, 56, 47

a)      Find first, second and third quartiles.

b)      Find interquartile range, Quartile deviation.

ANS:a) Data in arranged order: 47,48,49,50,51,52,53,54,55,56,57

           number of data points, n = 11

position of Q_i = i(n+1)/4

Position of Q1= (n+1)/4 = (11+1)/4 = 12/4= 3

So, Q1= 3^rd value

           = 49

Position of Q2= 2(11+1)/4 = 24/4 = 6

So, Q2= 6^th value

           = 52

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Position of Q3= 3(11+1)/4 = 36/4 =9

So, Q3= 9^th value

           55

b)  Interquartile range = Q3-Q1

                                    = 55-49 = 6

      Quartile deviation = (Q3-Q1)/2

                                    = (55-49)/2

                                    = 6/2 = 3

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