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 \(\boxed{0.175}\).