In order to determine the fraction of people who spent less than 20 minutes exercising, we need to follow these steps:
1. Identify the relevant frequencies:
We need to know the number of people who spent time in the intervals \(0 \leq t < 10\) and \(10 \leq t < 20\).
- For \(0 \leq t < 10\), the frequency is 4.
- For \(10 \leq t < 20\), the frequency is 11.
2. Calculate the total number of people who spent less than 20 minutes exercising:
Add the frequencies from the two relevant intervals:
[tex]\[
4 + 11 = 15
\][/tex]
So, 15 people spent less than 20 minutes exercising.
3. Calculate the total number of people surveyed:
Add up all the frequencies given in the table:
[tex]\[
4 + 11 + 9 + 8 + 3 = 35
\][/tex]
This gives us the total number of people surveyed.
4. Determine the fraction of people who spent less than 20 minutes exercising:
We need to form a fraction with the number of people who spent less than 20 minutes exercising (numerator) and the total number of people surveyed (denominator):
[tex]\[
\frac{15}{35}
\][/tex]
5. Simplify the fraction:
Simplify \(\frac{15}{35}\) by finding the greatest common divisor (GCD) of 15 and 35, which is 5. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{15 \div 5}{35 \div 5} = \frac{3}{7}
\][/tex]
Therefore, the fraction of people who spent less than 20 minutes exercising yesterday is [tex]\(\frac{3}{7}\)[/tex].
