The information in the table below was compiled from a national survey conducted
ID: 3221402 • Letter: T
Question
The information in the table below was compiled from a national survey conducted by a government agency of Caribbean state. The table represents the monthly income and educational levels for participants of a representative sample. The population for the survey represents all persons 15 years or older.
Income
Primary
Secondary
Undergraduate/Postgraduate
Less than $5000
55
25
13
$5000-$15000
17
18
66
$15000-$25000
7
9
25
Greater than $25000
2
5
10
(a) Define the term random variable and name the random variables in the table above.
(b) If a person 15 years or older is selected at random from the country, calculate the probability that this person earns an income that is between $15000 and $25000.
(c) What is the probability that a person 15 years or older selected at random completes a degree (Undergraduate/postgraduate)?
(d) Given that a person 15 years or older, has a primary education, what is the probability that this person earns a monthly income that is less than $5000?
(e) What percentage of the population 15 years or older who have a level of education higher than primary, given that the person earns an income that is greater than $25000.
Income
Primary
Secondary
Undergraduate/Postgraduate
Less than $5000
55
25
13
$5000-$15000
17
18
66
$15000-$25000
7
9
25
Greater than $25000
2
5
10
Explanation / Answer
Answer with explanations to all the part in detail:
a.
A random variable, usually written X, is a variable whose possible values are numerical outcomes of a random phenomenon. There are two types of random variables, discrete and continuous.
Here there are :
No. of primary
No. of Secondary
No. of Under/Postgraduate
b.
P( person is 15 years or older, his income between 15000 and 25000)=
(17+18+66)/(55+25+13+17+18+66+7+9+25+2+5+10)
=.40
c.
P( completes a degree)
= (13+66+25+10)/(55+25+13+17+18+66+7+9+25+2+5+10)
=.4523
d.
P( given he has primary edn, he earns less than 5000)
=55/(55+17+7+2)
=.679
d.
P(level of edn higher than primary given he earns>25000)
= has level above primary and earns more than 25000/ people who earn more than 25000
= (5+10)/(5+10+2)
= 0.8823
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