Researchers carried out a survey of fourth-, fifth-, and sixth-grade students in Michigan.

Tammy Todd 2020-10-19 Answered

Researchers carried out a survey of fourth-, fifth-, and sixth-grade students in Michigan. Students were asked whether good grades, athletic ability, or being popular was most important to them. This two-way table summarizes the survey data. 

Grade Mostimportant4th grade5th  grade 6th gradeTotalGrades495069168Athletic24363898Popular19222869Total92108135335 

 Suppose we select one of these students at random. What's the probability that: The student is a sixth grader or a student who rated good grades as important?

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Expert Answer

wheezym
Answered 2020-10-20 Author has 103 answers

Definitions: Completed rule P(Ac)=P(¬A)=1P(A) General addition rule for any two events:P(AorB)=P(A)+P(B)P(AandB)

Solution

Grade Mostimportant4th5th6th Total Grades495069168Athletic24363898Popular19222869Total92108135335

S = Sixth grader G = Grades We note that 135 of the 335 people in the table are 6th grades, because 135 is mentioned in the row ” Total” and in the column ”6th grade” of the given table. The probability is the number of favorable outcomes divided by the number of possible outcomes: P(5th grade)=#of favorable outcomes#of possible outcomes=135335 We note that 168 of the 335 people in the table rated good grades as important, because 168 is mentioned in the row ” Grades” and in the column ”Total” of the given table. P(Athletic and 5th grade)=#of favorable outcomes#of possible outcomes=168335 We note that 69 of the 335 people in the table are 6th graders who rated good grades as important, because 69 is mentioned in the row ” Grades” and in the column ”6th gradel” of the given table. P(G)=#of favor about comes#of possible out comes=69335 Use the general addition rule: P(SorG)=P(S)+P(G)P(SandG)
=135335+16833569335
=135+16869335
=234335
0.6985
=69.85%

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