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Thursday, January 13, 2011

MTH302- Business Mathematics & Statistics Complete Solved Final Term Paper

FINALTERM  EXAMINATION
Fall 2008
MTH302- Business Mathematics & Statistics (Session - 1)
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

       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
 
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
 
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.


   
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


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
             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 Qi = i(n+1)/4

Position of Q1= (n+1)/4 = (11+1)/4 = 12/4= 3
So, Q1= 3rd value
           = 49
Position of Q2= 2(11+1)/4 = 24/4 = 6
So, Q2= 6th value
           = 52

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