To solve this problem and determine the modal time taken to complete the first level in the new game, we will examine the provided data. The modal time is the time interval with the highest frequency, i.e., the interval during which the most players completed the first level.
Given the data:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Time Interval (minutes)} & \text{Number of Players} \\
\hline
35 < t < 45 & 5 \\
\hline
45 < t < 55 & 1 \\
\hline
55 < t < 65 & 15 \\
\hline
65 < t < 75 & 26 \\
\hline
75 < t < 85 & 19 \\
\hline
85 < t < 95 & 13 \\
\hline
95 < t < 105 & 6 \\
\hline
\end{array}
\][/tex]
Steps to find the modal time taken:
1. Identify the number of players for each time interval:
- For 35 < t < 45: 5 players
- For 45 < t < 55: 1 player
- For 55 < t < 65: 15 players
- For 65 < t < 75: 26 players
- For 75 < t < 85: 19 players
- For 85 < t < 95: 13 players
- For 95 < t < 105: 6 players
2. Find the maximum frequency:
- The maximum number of players (frequency) who completed the level falls in the interval 65 < t < 75 with 26 players.
3. Determine the modal interval:
- The interval with the highest frequency is 65 < t < 75.
Thus, the modal time taken for completing the first level in the game is between 65 and 75 minutes, with the number of players in this time interval being 26.
