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Conditional Probability Word Problems

Conditional Probability Word Problems
  • Page 1
 1.  
Select the statements related to descriptive statistics.
I. collection of data
II. organization and summarization of data
III. presentation of data
IV. determine relationships among variables of the data
a.
I and II only
b.
II and III only
c.
I, II and III only
d.
all are correct


Solution:

Descriptive statistics consists of collection, organization, summarization and presentation of data.

Inferential statistics determines the relationship between the variables of the data.

So, only I, II and III are related to descriptive statistics.


Correct answer : (3)
 2.  
Statistics find use in determining relationships among variables. Which of the following represent such cases?
I. use of coconut oil and heart attack
II. lung cancer and smokers
III. number of accidents on a highway
IV. monthly salary and annual salary
a.
I only
b.
I and II only
c.
I, II and III only
d.
all are correct


Solution:

Relation between use of coconut oil and its effects on heart attack can be determined using statistical study.

The chances of getting lung cancer due to smoking can be determined using statistical study.

Number of accidents on highway is only a data. There is no relationship between variables involoved in this case.

There is a direct relation between monthly salary and annual salary. There is no need for a statistical study in this case.

So, only I and II are correct.


Correct answer : (2)
 3.  
Which of the following are true for inferential statistics?
I. generalises from samples to population
II. uses probability
III. performs estimations and hypothesis to statistics
IV. makes predictions
a.
only I and III
b.
only II and IV
c.
only II, III and IV
d.
all are correct


Solution:

In inferential statistics, the statisticians try to make inferences.

Samples of the population are used for study.

Analysis is done through estimation, hypothesis tests, etc.

For making inferences or predictions, probability techniques are applied.

So, all the statements are correct.


Correct answer : (4)
 4.  
Select the statements where descriptive statistics is used.
I. Increase in the annual sales of hamburgers in the district was 30% of the sales of previous year.
II. Infant morality rate in an underdeveloped country registered a drop of 10% during the last decade.
III. Defence accounted 30% of the annual budget for the year 2003 - 2004.
IV. There are 1200 regular users of internet in a school of 2000 students.
a.
I, II and III only
b.
I, III and IV only
c.
IV only
d.
all are correct


Solution:

All the statements belong to descriptive statistics.


Correct answer : (4)
 5.  
Select the statements where inferential statistics is used.
I. The average annual salary of a software engineer in the age group of 23 - 25 is $50,000.
II. Increase in the price of steel from 1990 to 1995 was 37%.
III. The number of students getting enrolled in a university increases 10% every year.
IV. Number of mobile telephone connections in the country increased 20 times during the past 5 years.
a.
I only
b.
II and III only
c.
all are correct
d.
none of these


Solution:

All the statements are cases of descriptive statistics.

The cases of inferential statistics is none.


Correct answer : (4)
 6.  
Select the statements according to descriptive statistics (D) or inferential statistics (I).
1. 40 out of 100 heart patients admitted in a hospital were smokers.
2. Usage of a particular drug would reduce the number of heart attacks in the age group of 45 - 50 years.
3. The chances of getting a defective TV from a batch of 500 TV's dispatched from a manufacturing unit is 0.02.
a.
1 - D, 2 - D, 3 - I
b.
1 - D, 2 - I, 3 - I
c.
1 - I, 2 - I, 3 - I
d.
1 - I, 2 - I, 3 - D


Solution:

Statement 1 is descriptive statistics.

Statement 2 is made after study of a sample and arriving at an inference. It is inferential statistics.

Statement 3 is also a result of sampling and infering the result. It is also inferential statistics.


Correct answer : (2)
 7.  
Select the areas where probability is used.
I. insurance industry
II. end of the course examinations
III. weather predictions
IV. baseball game
a.
all are correct
b.
I and III only
c.
III and IV only
d.
I, III and IV only


Solution:

Insurance industry analyses the sample data from a population to arrive at the premium. Probability theory is applied in deciding the premium.

In the end of the course examinations, each answer sheet is valued. So there is no application of probability in this area.

Weather prediction applies probability theory.

Baseball game is a sport and not gambling. There is no application of probability in this game.


Correct answer : (2)
 8.  
Select the wrong statement(s).
I. Two major branches of statistics are statistics and probability.
II. A group of all subjects under study is called a population.
III. Statistics is the science of conducting studies to collect, organize, summarize, analyze and draw conclusions from data.
a.
I only
b.
II only
c.
I and II only
d.
all are wrong


Solution:

Two major branches of statistics are descriptive statistics and inferential statistics.

So, statement I is wrong.


Correct answer : (1)
 9.  
Select the qualitative variables.
I. School districts participating in the competition
II. Countries from which films are nominated for oscar awards
III. Religions represented in the ceremony
IV. Aggregate score of each student
a.
all
b.
I and III only
c.
II and III only
d.
I, II and III only


Solution:

Qualitative variables are variables which can be characterized according to some characteristics or attributes.

Variables under I, II and III are qualitative variables.


Correct answer : (4)
 10.  
Select the quantitative variables.
I. Monthly sales of each type of TV
II. Goals scored by each team in world cup soccer
III. Color of jerseys of each team in world cup soccer
IV. Medals won by each country in olympics
a.
I, II and III only
b.
I, II and IV only
c.
II, III and IV only
d.
all


Solution:

Quantitative variables are those which are numerical and can be ranked or ordered.

Variables under I, II and IV are quantitative variables.


Correct answer : (2)

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