Chapter 7, Problem 7.81RE

(a)

To determine

To Calculate: the probability that a randomly chosen student was in the bottom half of his or her high school class.

Answer to Problem 7.81RE

  $\text{P}\left(\text{D}\right)\text{=0}\text{.1}$

Explanation of Solution

Given:

Class Rank	Top 10%	Top quarter but not top 10%	Top half but not top quarter	Bottom half
Probability	0.3	0.3	0.3	?

Calculation:

Suppose

A = top 10%

B = top quarter but not top 10%

C = top half but not quarter

D = Bottom half

  $\begin{array}{c}\text{P}\left(\text{A}\right)\text{=0}\text{.3}\\ \text{P}\left(\text{B}\right)\text{=0}\text{.3}\\ \text{P}\left(\text{C}\right)\text{=0}\text{.3}\end{array}$

The addition of all probability should be 1 or 100%

  $\begin{array}{c}\text{P}\left(\text{D}\right)\text{=1-P}\left(\text{A}\right)\text{-P}\left(\text{B}\right)\text{-P}\left(\text{C}\right)\\ \text{=1-0}\text{.3-0}\text{.3-0}\text{.3}\\ \text{=0}\text{.1}\end{array}$

(b)

To determine

To Explain: that assign digits to represent the four possible outcomes listed.

Explanation of Solution

Given:

Class Rank	Top 10%	Top quarter but not top 10%	Top half but not top quarter	Bottom half
Probability	0.3	0.3	0.3	?

The probability of the top 10% is 0.3; it would be expected 3 out of 10 individuals to be in the top 10%. Similarly it would be expected 3 out of 10 individuals to be in the top half but not top quarter and it would be expected 1 out of 10 individuals to be in the bottom half.

10 possible digits

Top 10%:- 0, 1, 2

Top quarter but not top 10%:- 3, 4, 5

Top half but not top quarter: - 6, 7, 8

Bottom half: - 9