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
Q. The following system of equations illustrates the algebraic form of a partial (individual) market equilibrium model, which is a model of price (P) and quantity (Q) determination

While there are p original variables the number of principal components is m such that m

The mean tax-return preparation fee H&R Block charged retail customers in 2012 was $183 (The Wall Street Journal, March 7, 2012). Use this price as the population mean and assume t

Calculation for Continuous Series or Grouped Data = where, m = mid-point of class   =

In a three-cornered paint ball duel, A, B, and C successively take shots at each other until only one of them remains paint free. The three paint ballers have different probabiliti

Quota sampling Under this method enumerators shall select the respondents in place of those not available, as per the quota fixed according  to guide lines   provided to them.

Using log(x1), log(x2) and log(x3) as the predictors, do pair wise scatterplots of all pairs of variables (including the response) and comment (use the pairs function). Do you thin

A study was designed to investigate the effects of two variables - (1) a student's level of mathematical anxiety and (2) teaching method - on a student's achievement in a mathemati

As we stated above, we start factor analysis with principal component analysis, but we quickly diverge as we apply the a priori knowledge we brought to the problem. This knowled

To compare three brands of computer keyboards, four data entry specialists were randomly selected. Each specialist used all three keyboards to enter the same kind of text material