An empirical probability distribution based on weekly study times for a sample of 40 students is provided to the right. Suppose one of those students was chosen randomly. In parts (a) through (d) below, using your distribution, find the probability that the study time in the past week for the student selected would have been in each of the following ranges.
(a) $30-39$ hours
0.075 (Type an integer or a decimal.)
(b) 40-59 hours
\begin{tabular}{ccc}
\begin{tabular}{c}
Class \\
Limits
\end{tabular} & \begin{tabular}{c}
Frequency \\
$\mathbf{f}$
\end{tabular} & \begin{tabular}{c}
Relative \\
Frequency
\end{tabular} \\
$10-19$ & 8 & 0.200 \\
$20-29$ & 9 & 0.225 \\
$30-39$ & 6 & 0.150 \\
$40-49$ & 10 & 0.250 \\
$50-59$ & 2 & 0.050 \\
$60-69$ & 1 & 0.025 \\
$70-79$ & 4 & 0.100 \\
Total: & $\mathrm{n}=40$ &
\end{tabular}
(c) fewer than 30 hours
$\square$ (Type an integer or a decimal.)
(d) at least 50 hours
$\square$ (Type an integer or a decimal.)

Step 1 ：The question is asking for the probability of a student's study time falling within certain ranges. The probabilities are given by the relative frequencies in the provided table.

Step 2 ：For part (a), we need to find the relative frequency for the range 30-39 hours. From the table, this is \(0.15\).

Step 3 ：For part (b), we need to add the relative frequencies for the ranges 40-49 hours and 50-59 hours. From the table, these are \(0.25\) and \(0.05\) respectively. Adding these gives \(0.3\).

Step 4 ：For part (c), we need to add the relative frequencies for the ranges 10-19 hours and 20-29 hours. From the table, these are \(0.2\) and \(0.225\) respectively. Adding these gives \(0.425\).

Step 5 ：For part (d), we need to add the relative frequencies for the ranges 50-59 hours, 60-69 hours, and 70-79 hours. From the table, these are \(0.05\), \(0.025\), and \(0.1\) respectively. Adding these gives \(0.175\).

Step 6 ：Final Answer: (a) The probability that the study time in the past week for the student selected would have been in the range 30-39 hours is \(\boxed{0.15}\).

Step 7 ：(b) The probability that the study time in the past week for the student selected would have been in the range 40-59 hours is \(\boxed{0.3}\).

Step 8 ：(c) The probability that the study time in the past week for the student selected would have been fewer than 30 hours is \(\boxed{0.425}\).

Step 9 ：(d) The probability that the study time in the past week for the student selected would have been at least 50 hours is \(\boxed{0.175}\).