Question

yolanda wanted to see if there was a connection between red hair and green eyes. she observed people walking past her on the street and noted their hair and eye color. red hair green eyes: 18 eye color other than green: 29 hair color other than red green eyes: 114 eye color other than green: 650 consider the relative frequency table. to the nearest whole percent, what is the value of x in the table? x = 14% x = 15% x = 16% x = 18%

Explanation:

Step1: Calculate the total number of people

The total number of people is \(18 + 29+114 + 650=811\).

Step2: Calculate the relative frequency of red - haired people with green eyes

The formula for relative frequency is \(\text{Relative Frequency}=\frac{\text{Frequency of the category}}{\text{Total Frequency}}\).
For red - haired people with green eyes, the frequency is \(18\) and the total frequency is \(811\).
So, \(x=\frac{18}{811}\times100\).

$$x=\frac{1800}{811}\approx 2.22$$

(This is wrong. Wait, no. Wait, actually, the problem is about the relative frequency of red - haired people. The total number of red - haired people is \(18 + 29=47\), and the total number of people is \(18+29 + 114+650=811\). The formula for \(x\) (relative frequency of red - haired people) is \(x=\frac{47}{811}\times 100\).

$$x=\frac{4700}{811}\approx5.795$$

(This is also wrong. Wait, no, looking back at the problem. Wait, the original data: red - haired (green eyes: 18, non - green: 29), non - red - haired (green: 114, non - green: 650). The total number of people \(N=18 + 29+114+650=811\). The value of \(x\) is the relative frequency of red - haired people. The number of red - haired people \(n=18 + 29 = 47\). Then \(x=\frac{47}{811}\times100\approx5.795\) (wrong). Wait, no! Wait, the problem might be that \(x\) is the relative frequency of red - haired with green eyes among all people. \(x=\frac{18}{18 + 29+114+650}\times100=\frac{18}{811}\times100\approx2.22\) (wrong). Wait, no, looking at the options. Wait, another approach: total number of people \(=18+29 + 114+650=811\). If we consider the formula for percentage \(P=\frac{\text{part}}{\text{whole}}\times100\).
If \(x\) is the percentage of red - haired people (sum of red - haired green - eyed and red - haired non - green - eyed) among all people. \(x=\frac{18 + 29}{18+29+114+650}\times100=\frac{47}{811}\times100\approx5.795\) (not in options). Wait, no! Wait, maybe the problem is misread. Wait, the formula for \(x\) (if \(x\) is the percentage of red - haired with green eyes among all green - eyed people). The number of green - eyed people is \(18+114 = 132\). Then \(x=\frac{18}{18 + 114}\times100=\frac{18}{132}\times100=\frac{1800}{132}\approx13.64\approx14\).

Answer:

\(x = 14\%\)