To find the inequality range for race times, we must first arrange the times and find the median, which is 32 minutes. The desired race time with an absolute deviation of at most 5 minutes from the median results in the inequality 27 ≤ x ≤ 37.
Step-by-step explanation:
To solve this problem, we need to arrange the given race times in order and find the median. Once we find the median, we can set up an inequality that represents a race time within 5 minutes more or less than this median time.
First, we arrange the race times in ascending order: 20, 31, 27, 32, 25, 42, 48, 28, 40, 38, 32. After putting them in the proper order (20, 25, 27, 28, 31, 32, 32, 38, 40, 42, 48), we find that the median, which is the middle value, is 32 minutes since there are 11 times, and the 6th time is the median.
Next, we want to have a race time with an absolute deviation of at most 5 minutes from the median (32 minutes). This gives us the inequality 27 ≤ x ≤ 37. So, the time you hope to achieve in the race is between 27 and 37 minutes.