To determine the fraction of people who spent less than 20 minutes exercising yesterday, we need to follow these steps:
1. Compile the given frequencies:
- The number of people spending 0 to less than 10 minutes is 4.
- The number of people spending 10 to less than 20 minutes is 11.
- The number of people spending 20 to less than 30 minutes is 9.
- The number of people spending 30 to less than 40 minutes is 8.
2. Calculate the total number of people surveyed:
[tex]\[
\text{Total number of people} = 4 (0 \leq t < 10) + 11 (10 \leq t < 20) + 9 (20 \leq t < 30) + 8 (30 \leq t < 40) = 32
\][/tex]
3. Determine the number of people who spent less than 20 minutes exercising:
[tex]\[
\text{Number of people who spent less than 20 minutes} = 4 (0 \leq t < 10) + 11 (10 \leq t < 20) = 15
\][/tex]
4. Formulate the fraction of people who spent less than 20 minutes exercising:
[tex]\[
\text{Fraction of people} = \frac{\text{Number of people who spent less than 20 minutes}}{\text{Total number of people}} = \frac{15}{32}
\][/tex]
5. Ensure the fraction is in its simplest form:
The fraction [tex]\(\frac{15}{32}\)[/tex] is already in its simplest form because 15 and 32 have no common factors other than 1.
Therefore, the fraction of people who spent less than 20 minutes exercising yesterday is:
[tex]\[
\boxed{\frac{15}{32}}
\][/tex]
