To determine the probability that a student studied for exactly 5 hours, we need to follow these steps:
1. Find the Total Number of Students Surveyed:
To get the total number of students surveyed, we sum the number of students in each category.
[tex]\[
\begin{aligned}
1 + 3 + 3 + 10 + 9 + 6 + 3 = 35
\end{aligned}
\][/tex]
So, the total number of students surveyed is 35.
2. Identify the Number of Students who Studied for Exactly 5 Hours:
From the survey table, we can see that the number of students who studied for exactly 5 hours is 6.
3. Calculate the Probability:
The probability that a randomly selected student studied for exactly 5 hours is given by the ratio of the number of students who studied for 5 hours to the total number of students surveyed.
[tex]\[
\begin{aligned}
\text{Probability} &= \frac{\text{Number of students who studied for 5 hours}}{\text{Total number of students}} \\
&= \frac{6}{35}
\end{aligned}
\][/tex]
4. Rounding to the Nearest Hundredth:
To get the probability rounded to the nearest hundredth, we calculate:
[tex]\[
\frac{6}{35} \approx 0.171428571
\][/tex]
Rounded to the nearest hundredth, this is 0.17.
So, the probability that a student studied for exactly 5 hours is [tex]\( 0.17 \)[/tex].
