To determine the percentage of people surveyed who have basketball shoes, we need to analyze the relative frequency table provided. The table tells us the following information:
- The relative frequency of customers who have both running shoes and basketball shoes is 0.23.
- The relative frequency of customers who have basketball shoes but no running shoes is 0.31.
To find the total relative frequency of customers who have basketball shoes (regardless of whether they have running shoes or not), we add these two relative frequencies together:
[tex]\[ \text{Total relative frequency of having basketball shoes} = 0.23 + 0.31 \][/tex]
When we perform the addition, we get:
[tex]\[ 0.23 + 0.31 = 0.54 \][/tex]
This relative frequency of 0.54 represents the proportion of the surveyed population that has basketball shoes.
To convert this relative frequency to a percentage, we multiply by 100:
[tex]\[ \text{Percentage of people with basketball shoes} = 0.54 \times 100 \][/tex]
Performing the multiplication:
[tex]\[ 0.54 \times 100 = 54 \][/tex]
Therefore, [tex]\(54\% \)[/tex] of the people surveyed have basketball shoes.
So, the correct answer is:
D. [tex]\(54 \%\)[/tex]
