Question

As part of a class project, a university student surveyed the students in the cafeteria lunch line to look for a relationship between eye color and hair color among students. The table below contains the results of the survey. Eye Color Hair Color Blue Gray Green Brown Marginal Totals Blond 42 5 21 10 78 Red 12 22 19 12 65 Brown 22 5 12 34 73 Black 9 3 11 64 87 Marginal Totals 85 35 63 120 303 From the sample population of students with gray eyes, what is the relative frequency of students with red hair?

Answer 1

The relative frequency of students with red hair among the sample population of students with gray eyes is approximately 62.86%.

The relative frequency of students with red hair among the sample population of students with gray eyes can be calculated by considering the intersection of the "Gray Eyes" row and the "Red Hair" column in the given table.

From the table:

The number of students with gray eyes is 35.

The number of students with red hair and gray eyes is 22.

The relative frequency is calculated by dividing the number of students with red hair and gray eyes by the total number of students with gray eyes.

Relative Frequency = Number of Students with Red Hair and Gray Eyes / Total Number of Students with Gray Eyes

Relative Frequency = 22 / 35

Simplifying the fraction:

Relative Frequency is approximately 0.6286 or 62.86%.

Answer 2

The table is attached below

We need to find the relative frequency of students with red hair from the students with gray eyes.

From the table we can see that the total number of students with gray eyes is 35. then the number of red hair students with gray eye is 22

the relative frequency of students with red hair = Total students of red hair with gray eyes divide by total number of gray eye students

=
`(22)/(35)=0.628571428 = 0.63`

Answer is 0.63