## The bulbs manufactured by a company

## Quantitative Methods

**Questions:**

**CASE 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.

#### 2) In what situation does one need probability theory?

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

#### 4) What is the difference between objective and subjective probability?

**CASE 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.

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

#### 3) What is a simple linear regression model?

#### 4) What is a scatter diagram method?

**CASE 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.

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

#### 3) What is the Future Value of money.

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

**CASE 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?

#### 2) What is a chi-square test?

#### 3) What is sampling and what are its uses.

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

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