Quantitative Methods

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SUBJECT : Quantitative Methods 

COURSE :  MBA 4th Semester                                   Total Marks : 80

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CASE STUDY: 1

The bulbs manufactured by a company gave a mean life of 3000 hours with standard deviation of 400 hours. If a bulb is selected at random, what is the probability it will have a mean life less than 2000 hours?

1)    Calculate the probability.

Ans. P(x < 2000) =?

In what situation does one need probability theory?

Ans. Probability theory is applied to situations where uncertainty exists. These situations include

1.  The characterization of traffic at the intersection US 460 and Peppers Ferry Road (i.e., the number of cars that cross the intersection as a function of time).

2.  The prediction of the weather in Blacksburg.

3.  The number of

2)    Define the concept of sample space, sample points and events in context of probability theory.

Ans. sample spaceà Definition:   The sample space of an experiment is the set of all possible outcomes of that experiment.

3)    What is the difference between objective and subjective probability?

Ans.  Objective probability is where I know that if I toss a fair coin enough times, it’ll turn up heads 50% of the time. Subjective probability is where I think there’s a 10% chance it’ll rain tomorrow, and I don’t care to repeat the event. The former is an informed statement about a system. The latter is our best guess about an event. The former number is a constant, if we’ve done the calculations right.

CASE STUDY: 2

The price P per unit at which a company can sell all that it produces is given by the function P(x) = 300 — 4x. The cost function is c(x) = 500 + 28x where x is the number of units produced. Find x so that the profit is maximum.

1)    Find the value of x.

Ans. profit = sales-cost
sales=quantity*price = x (300-4x)
cost = 500+28x

2)    In using regression analysis for making predictions what are the assumptions involved.

Ans. I computed a simple linear regression model from my experiment measures in order to make predictions. I have read that you should not calculate predictions for points that depart too far from the available data. However, I could not find any

.

3)    What is a simple linear regression model?

Ans. simple linear regression is the least squares estimator of a linear regression model with a single explanatory variable. In other words, simple linear regression fits a straight line through the set of n points in such a way that makes the sum of squared residuals of the model (that is,

4)    What is a scatter diagram method?

Ans. Scatter graph method is a graphical technique of separating fixed and variable components of mixed cost by plotting activity level along x-axis and corresponding total cost (mixed cost) along y-axis. A regression line is then drawn on the graph by visual inspection. The line thus drawn is used to estimate the total fixed cost and variable cost per unit. The point where the line intercepts y-axis is the estimated fixed cost and the slope of the line is the average variable

CASE STUDY: 3

Mr. Sehwag invests Rs 2000 every year with a company, which pays interest at 10% p.a. He allows his deposit to accumulate at C.I. Find the amount to the credit of the person at the end of 5th year.

1)    What is the Time Value of Money concept?

Ans. The time value of money is the principle that the purchasing power of money can vary over time; money today might have a different purchasing power than money a decade later. The value of money at a future point in time might be

2)    What do you mean by present value of money?

Ans. The current worth of a future sum of money or stream of cash flows given a specified rate of return. Future cash flows are discounted at the discount rate, and the higher the discount rate, the lower the present value of the future cash flows.

3)    What is the Future Value of money?

Ans. The value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today. There are two ways to calculate FV:

1) For an asset with simple

4) What the amount to be credited at the end of 5th year.

Ans.

CASE STUDY: 4

The cost of fuel in running of an engine is proportional to the square of the speed and is Rs 48 per hour for speed of 16 kilometers per hour. Other expenses amount to Rs 300 per hour. What is the most economical speed?

1)    What is most economical speed?

Ans. Based on the above statement, the formula for cost is 
C = k*v2 + 300. 
So, for 48 rs per hour cost at 16 per hour

2)    What is a chi-square test?

Ans. A chi-squared test, also referred to as chi-square test or χ² test, is any statistical hypothesis test in which the sampling distribution of the test statistic is a chi-squared distribution when the null hypothesis is true. Also considered a chi-squared test is a test in which this is asymptotically true, meaning that the sampling distribution (if

3)    What is sampling and what are its uses.

Ans. A process used in statistical analysis in which a predetermined number of observations will be taken from a larger population. The methodology used to sample from a larger population will depend on the type of analysis being performed, but will include simple random sampling, systematic sampling and observational sampling.

The sample sho

4)Is there any alternative formula to find the value of Chi-square?

Ans. The Formula for Chi-Square Statistic

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