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?
Question:
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 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.
Question:
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 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.
Question :
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 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?
Question:
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
CASE STUDY: 1
1) To calculate the probability, we need to use the concept of z-score. The z-score represents the number of standard deviations a particular value is away from the mean. In this case, we want to find the probability that a bulb will have a mean life less than 2000 hours.
First, we need to calculate the z-score using the formula: z = (x - μ) / σ
where x is the value we want to find the probability for (2000 hours), μ is the mean (3000 hours), and σ is the standard deviation (400 hours).
Substituting the values, we get: z = (2000 - 3000) / 400 = -2.5
Next, we need to find the probability using the z-score. We can use a standard normal distribution table or a calculator to find the corresponding probability. Looking up the z-score of -2.5 in the table, we find that the probability is approximately 0.0062 or 0.62%.
Therefore, the probability that a bulb will have a mean life less than 2000 hours is approximately 0.0062 or 0.62%.
2) Probability theory is needed in situations where uncertainty exists and we want to make predictions or determine the likelihood of certain events occurring. It is used in various fields such as statistics, economics, finance, physics, and many more. For example, in business, probability theory can help in making decisions about investments, analyzing market trends, and assessing risks.
3) In probability theory, the sample space is the set of all possible outcomes of an experiment. Sample points are the individual outcomes within the sample space. For example, if a coin is flipped, the sample space would consist of two sample points: heads and tails. An event is a subset of the sample space, which consists of one or more sample points. In the case of the bulb's mean life, an event could be the bulb having a mean life less than 2000 hours.
4) Objective probability refers to probabilities that can be calculated or determined based on facts, data, and mathematical calculations. It is based on objective evidence or observations. Subjective probability, on the other hand, is based on personal opinions, beliefs, or judgments. It involves assigning probabilities subjectively without relying on concrete evidence or data. It can differ from person to person based on their individual perceptions or biases.