Introduction to probability, Applied Statistics

Introduction to Probability

A student is considering whether she should enroll in an MBA educational program offered by a well-known college. Among other things, she would like to know how difficult the program is she obtains the following marks distribution of students who appeared for the most final examination in the previous year.

Relative Frequency Distribution

Marks %

No. of students

% of students

0   - 25

 45

 8

25 - 50

280

50

50 - 75

205

37

75 - 100

30

 5

 

560

100

Assuming the next exam is equally tough and there are same proportion of dull and bright students, she may conclude that the percentage of students in the four classes of marks will again be

Marks %

% of students

0   - 25

8

25 - 50

50

50 - 75

37

75 - 100

5

 

100

The first distribution above is related to past data and is a frequency distribution. The second distribution has the same numbers and is a copy of the first distribution. However, this distribution relates to the future. Such a distribution is called a probability distribution. Note the similarity of this distribution with that of the relative frequency distribution.

Hence by inspecting the probability distribution we can say that:

8% of the students who are appearing for the exam will score 0 - 25% marks, 50% will score 25 - 50% marks, 37% will score 50 - 75% marks and the balance 5% will score 75 - 100% marks.

If our student considers herself to be among the top 5% of the students, she can conclude that she will score 75 - 100% marks. If she considers herself to be in the top 42% of students she can conclude that she will score 50 - 100% marks and so on. However, if she has no idea of her ability in relation to the other students she can conclude that:

She has an 8% chance of scoring 0 - 25% marks, a 50% chance of scoring
25 - 50% marks, a 37% chance of scoring 50 - 75% marks and a 5% chance of scoring 75 - 100% marks. This "chance" is called probability in statistical language.

Probability theory is used to analyze data for decision making.

The insurance industry uses probability theory to calculate premium rates. A stock analyst/investor, based on the probability estimates of economic scenarios and estimates the returns of the stocks. A project manager applies probability theory in decision-making.

Posted Date: 9/14/2012 4:08:30 AM | Location : United States







Related Discussions:- Introduction to probability, Assignment Help, Ask Question on Introduction to probability, Get Answer, Expert's Help, Introduction to probability Discussions

Write discussion on Introduction to probability
Your posts are moderated
Related Questions
#questionMaximize Z= 3x1 + 2X2 Subject to the constraints: X1+ X2 = 4 X1 - X2 = 2 X1, X2 = 0..


Why are graphs and tables useful when examining data? A researcher is comparing two middle school 7th grade classes. One class at one school has participated in an arts program

what is the aim of statistics?

For each of the following scenarios, explain how graph theory could be used to model the problem described and what a solution to the problem corresponds to in your graph model.

Calculation of Degrees of Freedom First we look at how to calculate the number of DOF for the numerator. In the numerator since we calculate the variance from the sample means,

What would be the cutoff score to indicate a score that is in the top 15% of the scores on a test with a mean of 100 and a standard deviation of 15? This question has multiple p

Q. Find relative maxima and minima? When finding relative maxima and minima in the Chapters absolute extrema problem, don't forget to use the first or second derivative test to

Scenario: Many of the years 5 and year 6 learners' at Woodlands Park School were excited about being chosen for the cross-country team.  Every day, they were able to run laps of t

"MagTek" electronics has developed a smart phone that does things that no other phone yetreleased into the market-place will do. The marketing department is planning to demonstrate