MID AND FINAL TERM PAPERS OF MTH302

FINALTERM EXAMINATION
Spring 2009
MTH302- Business Mathematics & Statistics

Time: 120 min
Marks: 80

Question No: 1 ( Marks: 1 ) - Please choose one
The Basic salary of an employee is Rs 7,000. What is the contribution of the company
on account of gratuity to the Gratuity Trust Fund?

• Rs 636.36
• Rs 6363.6
• Rs 63.636
• Rs 6363

Question No: 2 ( Marks: 1 ) - Please choose one
An arrangement of data by successive time periods is called a

• Exponential Smoothing
• Time Series
• Combination
• Permutation

Question No: 3 ( Marks: 1 ) - Please choose one
The graph of time series is called

• Straight line
• Smooth Curve
• Parabola
• Histogram

Question No: 4 ( Marks: 1 ) - Please choose one
When a straight is fitted to time series data, it is called

• Linear equation
• Linear regression
• Linear trend
• Non-Linear equation

Question No: 5 ( Marks: 1 ) - Please choose one
What variation does moving averagemethod eliminate?

• Seasonal
• Cyclical
• Irregular
• Secular trend

Question No: 6 ( Marks: 1 ) - Please choose one
The temperature was 30°C in the afternoon and the temperature dropped to 26°C in the
evening. Find the percentage change in the temperature.

• 13.33%
• 15%
• 14.26%
• 12%

Question No: 7 ( Marks: 1 ) - Please choose one
Observed errors, which represent information from the data which is not explained by
the model, are called?

• Marginal values
• Residuals
• Mean square errors
• Standard errors

Question No: 8 ( Marks: 1 ) - Please choose one
An insurance company wants to predict sales from the amount of money they spend on
advertising. Which would be the independent variable?

• sales
• advertising
• insufficient information to decide
• Both (i) and (ii) are correct.

Question No: 9 ( Marks: 1 ) - Please choose one
Frequency of occurrence is used in finding the

• weighted mean
• median
• mode
• variance

Question No: 10 ( Marks: 1 ) - Please choose one
If the equation of regression line is y = 5, then what result will you take out from it?

• The line passes through origin.
• The line passes through (5, 0)
• The line is parallel to y-axis.
• The line is parallel to x-axis

Question No: 11 ( Marks: 1 ) - Please choose one
Which of the following graphs is a visual presentation using horizontal or vertical bars to
make comparisons or to show relationships on items of similar makeup?

• bar graph
• pie graph
• pictograph
• line graph

Question No: 12 ( Marks: 1 ) - Please choose one
In how many ways can the letters of the word MANAGEMENT be rearranged so that
the two As do not appear together?

• 10! - 2!
• 9! - 2!
• 10! - 9!
• None of these

Question No: 13 ( Marks: 1 ) - Please choose one
Which of the following describe the middle part of a group of numbers?

• Measures of central tendency
• measures of variability
• measures of shape
• measures of association

Question No: 14 ( Marks: 1 ) - Please choose one
In the United States, 43% of people wear a seat belt while driving. If two people are chosen at random, what is the probability that both of them wear a seat belt?

• 18%
• 20%
• 25%
• None of these

Question No: 15 ( Marks: 1 ) - Please choose one
The midrange is not greatly affected by outliers

• False
• True

Question No: 16 ( Marks: 1 ) - Please choose one
In which of the following form, can the probability be written?

• fraction
• decimal
• percentage
• All of these.

Question No: 17 ( Marks: 1 ) - Please choose one
The moving averages of the Prices 90,70,30,110 are

• 63.33, 70
• 73.33,80
• 45.45, 68
• 65.50, 75

Question No: 18 ( Marks: 1 ) - Please choose one
Sum of annuity is always

• Present value
• Future value
• Net present value
• Current value

Question No: 19 ( Marks: 1 ) - Please choose one
Write a formula to find the simple interest (I) if $5000 is invested at 4% for 2 years.

• I=PRT
• I=P+R+T
• I=PT
• I=P(R+T)

Question No: 20 ( Marks: 1 ) - Please choose one
Solve 3x = 27 for x

• 0.9
• 6
• 18
• 9

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

 

In regression analysis, when we plot the values of dependent and independent variables, the resulting set of points is called

       ► Scatter Diagram

       ► Venn diagram

       ► Histogram

       ► Pie Graph

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

 

Slope of the line passing through the points A (2, 3) and B (3, 4) is

       ► Zero

       ► One

       ► Two

       ► Three

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

 

A significant value of a correlation coefficient calculated from a sample of data

 (x, y) implies that                          

       ► x causes y

       ► y causes x

       ► x and y have a curved relationship

       ► x and y have a relationship with a strong linear component

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

 

The measure of how well the regression line fits the data is the:

       ► coefficient of determination

       ► slope of the regression line

       ► mean square error

       ► standard error of the regression coefficient

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

 

What is the slope of the line y = -3.4x - 2.5?

       ► -2.5

       ► 2.5

       ► -3.4

       ► 3.4

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

 

My estimated regression line is Y = 17 + 4X. The intercept is equal to:

       ► 17

       ► 4

       ► 21

       ► 13

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

 

How many arrangements can be made of the letter MOVING  

       ► 900

       ► 120

       ► 600

       ► 720

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

 

Which of the following statements is true regarding the standard deviation?

       ► It cannot assume a negative value.

       ► If it is zero, then all the data values are the same

       ► It is in the same units as the mean.

       ► All the given choices are correct

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

 

There are 5 Rock songs, 6 Carnatic songs and 3 Indian pop songs. How many different albums can be formed using the above repertoire if the albums should contain at least 1 Rock song and 1 Carnatic song?

       ► 15624

       ► 16384

       ► 6144

       ► 240

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

 

In what range does correlation coefficient lie?

       ► 0 to +1

       ► -1 to 0

       ► -1 to +1

       ► Greater than 1

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

 

Which of the following describe the middle part of a group of numbers?

       ► Measures of central tendency

       ► measures of variability

       ► measures of shape

       ► measures of association

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

 

Evaluate

       ► 0

       ► 10

       ► 120

       ► 720

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

 

Evaluate 

       ► n

       ► one

       ► Zero

       ►

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

 

A large basket of fruit contains 3 oranges, 2 apples and 5 bananas. If a piece of fruit is chosen at random, what is the probability of getting an orange or a banana?

       ► 1/2

       ► 5/4

       ► 4/5

       ► 1/7

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

 

In the United States, 43% of people wear a seat belt while driving. If two people are chosen at random, what is the probability that both of them wear a seat belt?

       ► 18%

       ► 20%

       ► 25%

       ► None of these

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

 

The formula to calculate Mean squared deviation from the mean is

       ►

       ►

       ►

       ►

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

 

Suppose we developed the following least squares regression equation: Y= 3 + 2X. Which of the following statements are correct?

       ► The dependent variable increases 2 for an increase of 1 in X

       ► The equation crosses the Y-axis at 3.5

       ► If X = 5, then Y = 14.

       ► Y is independent variable

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

 

The median in an odd number of values is the ------------ value.

       ► first

       ► middle

       ► last

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

 

The ------------------ indicates where the center of data occurs without distorting a group of numbers with one or more extreme values.

       ► median

       ► mode

       ► mean

       ► quartile

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

 

The --------------- is intended to measure the spread of the data about the mean.

       ► mean

       ► median

       ► mode

       ► standard deviation

Question No: 21      ( Marks: 1 ) - Please choose one

 

In which of the following form, can the probability be written? 

       ► fraction

       ► decimal

       ► percentage

       ► All of these.

Question No: 22      ( Marks: 1 ) - Please choose one

 

Principal remains constant through out the agreement period in:

       ► Compound interest

       ► Annuity

       ► Simple interest

       ► Nominal interest

Question No: 23      ( Marks: 1 ) - Please choose one

 

If A and B are any two matrices of order  and  respectively and m>n and p<q. What should be the condition on m, n, p, q for the product AB to hold?

       ► n>p

       ► m<=q

       ► q=p

       ► n=p

Question No: 24      ( 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: 25      ( Marks: 1 ) - Please choose one

 

The mode of the words in the word  CORRELATION is

       ► L

       ► R

       ► O

       ► Both R and O

Question No: 26      ( Marks: 1 ) - Please choose one

 

The correct relation among the %markup on cost, cost price and selling price is

       ► Selling Price = Cost price + (Cost price × %Markup on sale)

       ► Selling Price = Cost price + (Cost price × %Markup on cost)

       ► Cost Price = selling price + (Cost price × %Markup on cost)

       ► None of these

Question No: 27      ( Marks: 1 ) - Please choose one

 

To add numbers based on multiple conditions we use

       ► IF and SUM functions .

       ► DSUM function.

       ► AVERAGE function.

       ► All functions given in above choices .

Question No: 28      ( Marks: 1 ) - Please choose one

 

If A= [a b c] is a matrix then in order to find AB, the number of columns B must have are

       ► 3

       ► 1

       ► 2

       ► any non zero number

Question No: 29      ( Marks: 1 ) - Please choose one

 

Given  FC = Rs.5000 ,CM= Rs. 30 ,VC= Rs. 150 , Capacity = 320units then BEP in units =   

       ► 4500 units

       ► 167 units

       ► 33 units

       ► 16 units

Question No: 30      ( Marks: 1 ) - Please choose one

 

Actual = …

   

       ► Random - expected

       ► Random * expected

       ► Random + expected

       ► Random / expected

Question No: 31      ( Marks: 1 ) - Please choose one

 

An equation for the intercept of the regression line is:

       ►

       ►

       ►

       ►

Question No: 32      ( Marks: 1 ) - Please choose one

 

The ratio of the standard deviation of a distribution to the mean of that distribution is referred to as

       ► a probability distribution.

       ►  the expected return.

       ► the standard deviation.

       ►  coefficient of variation.

Question No: 33      ( Marks: 1 ) - Please choose one

 

Coefficient of variation shows dispersion of the

       ► standard deviation about mean.

       ► standard deviation about mode.

       ► variance about mean.

       ► variance about mode.

Question No: 34      ( Marks: 1 ) - Please choose one

 

The Excel function =POISSON (2, 5, True) is used to calculate ------------------------

       ► Normal Distribution

       ► Binomial Distribution

       ► Poisson Distribution

       ► Cumulative Poisson Distribution

Question No: 35      ( Marks: 1 ) - Please choose one

 

The graph which uses circles to represent a set of data is called

       ► Travel graph

       ► Picture graph

       ► Sector graph

       ► Cumulative distribution

Question No: 36      ( Marks: 1 ) - Please choose one

 

Is every Linear Programming has solution?

       ► true

       ► false

       ► may or may not

       ► none of these

Question No: 37      ( Marks: 1 ) - Please choose one

 

Returns the cumulative interest paid on a loan between start period and end period is ………

       ► CUMIPMT

       ► CUMPRINC

       ► FV

       ► PV

Question No: 38      ( Marks: 1 ) - Please choose one

 

The price after deduction of all discounts or allowances is known as…….

       ► net price

       ► new price

       ► list price

       ►  none of these

Question No: 39      ( Marks: 1 ) - Please choose one

 

Net income can be calculated by using

       ► Net income = Number of units sale above break even point * Price per unit

       ► Net income = Total number of units sold * Price per unit

       ► Net income = Number of units sale above break even point * contribution margin per unit

       ► Net income = Total number of units sold * contribution margin per unit.

Question No: 40      ( Marks: 1 ) - Please choose one

 

A single die is rolled.What is the probability of a 2 turning up.

       ► The answer is 1/6

       ► The answer is 2/6

       ► The answer is 0

       ► The answer is 1

Question No: 41      ( Marks: 2 )

 

If Y = 5 + b X, find the value of b when Y = 9 and x = 2.

Solution:

Y=5+b X

Y-5=b X

b = (Y-5)/X

Putting the given value:

b = (9-5)/2

b = 4/2

b= 2    Ans.

Question No: 42      ( Marks: 2 )

 

What is most common measure of central tendency and how it is calculated?

Answer:

 Central Tendency refers to middle value and most  common measure of central tendency is the “Mean”.

Mean is calculated as follows:

Mean= (The sum of all values)/(The Number of Values)

Question No: 43      ( Marks: 2 )

 

In which condition none of the hypothesis testing procedures can be safely used.

Answer:

In the null hypothesis we don’t consider about proving null hypothesis and we must begin with assumption that there is no change at all.

Question No: 44      ( Marks: 3 )

 

A local trade union consists of plumbers and electricians. Classified according to rank:

                     Apprentice    Journeyman      Master

                      ------------------------------------

        Plumbers          25      |     20       |    30      75

                      ------------------------------------

        Electricians      15      |     40       |    20      75

                      -------------------------------------

                          40            60            50

A member of the union is selected at random.  Given that the

Person selected is a plumber, find the probability that he is a

Journeyman 

Question No: 45      ( Marks: 3 )

 

Calculate the mean deviation from mean = 30  of the following set of examination marks

28,30,32

Mean deviation        = x Mean/n

                                    = 30/3

                                    =10 marks

Question No: 46      ( Marks: 3 )

 

If a pollster might want to know whether or not, say, the sex, the ethnic background or salary range of a person is factor in his or her vote in election or for some type of legislation then justify which distribution is best fit for this scenario?(least two sentence description )

Question No: 47      ( Marks: 5 )

 

Find the mean, median, mode, and range for the following list of values:

1, 2, 4, 7

Answer:

1. Mean               = (1+2+4+7)/4

=14/4

=3.5

2. Median            =(n+1)/2

                        =(4+1)/2

                        =5/2

                        =2.5^th Value is the median

We take average of 2^nd and 3^rd Value.

                        =(2+4)/2

                        =6/2

Median            =3

3. Mode               = None
4. Range              = Maximum Value-Minimum Value

= 7-1= 6

           

Question No: 48      ( Marks: 5 )

 

A die is rolled and a coin is tossed, find the probability that the die shows an odd number and the coin shows a head

Answer:

Die show odd number = 3/6

Coin Shows a head = 1/2

Probability of odd number and head of coin  =3/6 x 1/2

                                                                        =3/12

                                                                        =1/4

Question No: 49      ( Marks: 5 )

 

A random sample of 36 drinks from a soft drink machine has an average content 7.6 ounces with an standard deviation of 0.48 ounces. Test the hypothesis  ounces against the alternative hypothesis   at the 0.05 level of significance.

Question No: 50      ( Marks: 10 )

 

The probability that a student is accepted to a prestigeous college is 0.3. If 5 students from the same school apply, what is the probability that at most 2 are accepted