Statistics

Statistics

1. Coffee and Soft Drinks

Suppose 55 percent of adults drink coffee, 45 percent drink soft drinks, and 10 percent drink both.{Coffee and Soft Drinks Narrative} What is the probability that a randomly chosen adult does not drink soft drinks?

Solution

Coffee used = 55% people

Soft Drinks used = 45% people

Both = 10% people

The total usage of coffee and soft drink are = .55 + .45 = .90

The total probability is =1-0.90 = 0.10

The probability of adult that does not drink soft drink is = 0.10 (Bragg, 2007)

2. GPA and Class

A statistics professor classifies his students according to their grade point average (GPA) and their class rank. GPA is on a 0.0-4.0 scale, and class rank is defined as the underclass (freshmen and sophomores) and the upper class (juniors and seniors). One student is selected at random.

GPA

ClassUnder 2.02.0 - 3.0Over 3.0

Under0.050.250.10

Upper0.100.300.20

{GPA and Class Narrative} If the student selected is in the upper class, what is the probability that her GPA is between 2.0 and 3.0?

0.05 (The probability between 2.0 and 3.0 GP)

{GPA and Class Narrative} What is the probability that the student is in the lower class and has GPA over 3.0?

0.1333 (The probability that the student is in the lower class and has GPA over 3.0

3. Real Estate

The joint probability distribution of variables X and Y is shown in the table below. Amber and Bianca are real estate agents. Let X denote the number of houses that Amber will sell in a month, and let Y denote the number of houses Bianca will sell in a month.

X

Y123

10.300.180.12

20.150.090.06

30.050.030.02

{Real Estate Narrative} Determine the marginal probability distribution of X.

{Real Estate Narrative} Calculate E(X) and E(Y).

Solution:

 

X

 

 

marginal of y

Y

1

2

3

 

1

0.3

0.18

0.12

0.6

2

0.15

0.09

0.06

0.3

3

0.05

0.03

0.02

0.1

marginal of x

0.5

0.3

0.2

1

E(x) = Summation of X

= 1.7

E(Y) = Summation of Y

= 1.5

4. Lamps Lifetime

A certain brand of flood lamps has a lifetime that has ...