Chapter 7.2, Problem 7.45E

(a)

To determine

To Explain: the individuals and the variables which are measured.

Answer to Problem 7.45E

Individuals: 335 4^th, 5th and 6^th grade students in Michigan.

Variables: Most important (grades/athletic/popular) and grade (4/5/6).

Explanation of Solution

Given:

	4th Grade	5th Grade	6th Grade	Total
Grades	49	50	69	168
Athletic	24	36	38	98
Popular	19	22	28	69
Total	92	108	135	335

On the basis of given data

Individuals are 335 4^th, 5th and 6^th grade students in Michigan.

Variables are most important (grades/athletic/popular) and grade (4/5/6).

(b)

To determine

To Calculate: the probability if randomly selects a survey.

Answer to Problem 7.45E

  $\begin{array}{c}\text{P}\left(\text{6th}\right)\text{=0}\text{.403}\\ \text{P}\left(\text{grades}\right)\text{=0}\text{.5015}\\ \text{P}\left(\text{6th}\text{and}\text{grades}\right)\text{=0}\text{.206}\\ \text{P}\left(\text{6th}\text{or}\text{grades}\right)\text{=0}\text{.6985}\end{array}$

Explanation of Solution

Given:

	4th Grade	5th Grade	6th Grade	Total
Grades	49	50	69	168
Athletic	24	36	38	98
Popular	19	22	28	69
Total	92	108	135	335

Formula used:

  $\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}$

Calculation:

Required Probability using this table

  $\begin{array}{c}\text{P}\left(\text{6th}\right)\text{=}\frac{\text{135}}{\text{335}}\\ \text{=0}\text{.403}\\ \text{P}\left(\text{grades}\right)\text{=}\frac{\text{168}}{\text{335}}\\ \text{=0}\text{.5015}\\ \text{P}\left(\text{6th}\text{and}\text{grades}\right)\text{=}\frac{\text{69}}{\text{335}}\\ \text{=0}\text{.206}\\ \text{P}\left(\text{6th}\text{or}\text{grades}\right)\text{=}\frac{\text{49+50+69+38+28}}{\text{335}}\\ \text{=}\frac{\text{234}}{\text{335}}\\ \text{=0}\text{.6985}\end{array}$

(c)

To determine

To Calculate: the two-way table in this exercise different form the ones saw in earlier examples.

Explanation of Solution

Every variable has 3 possibilities instead of 2 where three variables are Grades, Athletic Popular and its possibilities are 4^th grade, 5^th grade and 6^th grade respectively.