To represent Blanca's lap times for the three days of practice with a histogram, we need to follow several steps involving the combination of data and distribution of that data into bins. Here is a detailed step-by-step solution to derive the necessary histogram:
1. Combine All Lap Times:
- For Day 1: [83, 92, 91, 89, 94, 93, 88, 84]
- For Day 2: [87, 90, 92, 91, 92, 95, 90, 85]
- For Day 3: [85, 86, 91, 93, 91, 89, 88, 84]
Combining these lists together, we get:
```
all_lap_times = [83, 92, 91, 89, 94, 93, 88, 84, 87, 90, 92, 91, 92, 95, 90, 85, 85, 86, 91, 93, 91, 89, 88, 84]
```
2. Define Bins for the Histogram:
To cover the range of lap times, we choose the following bins:
```
bins = [80, 82, 84, 86, 88, 90, 92, 94, 96]
```
3. Count Lap Times in Each Bin:
The bins will now be used to count the number of lap times that fall into each range:
- Bin [80, 82): 0 laps
- Bin [82, 84): 1 lap
- Bin [84, 86): 4 laps
- Bin [86, 88): 2 laps
- Bin [88, 90): 4 laps
- Bin [90, 92): 6 laps
- Bin [92, 94): 5 laps
- Bin [94, 96): 2 laps
Therefore, the histogram counts are:
```
histogram = [0, 1, 4, 2, 4, 6, 5, 2]
```
4. Edges of Each Bin:
The edges of the bins are:
```
bin_edges = [80, 82, 84, 86, 88, 90, 92, 94, 96]
```
Given these counts and bin edges, our final histogram would look as follows:
- Bin 80-82: 0 laps
- Bin 82-84: 1 lap
- Bin 84-86: 4 laps
- Bin 86-88: 2 laps
- Bin 88-90: 4 laps
- Bin 90-92: 6 laps
- Bin 92-94: 5 laps
- Bin 94-96: 2 laps
This representation matches the numerical result achieved, confirming that it is accurate. Thus, the correct histogram for Blanca's lap times over the three days is represented by:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|c|c|}
\hline \text{Bin Range} & 80-82 & 82-84 & 84-86 & 86-88 & 88-90 & 90-92 & 92-94 & 94-96 \\
\hline \text{Counts} & 0 & 1 & 4 & 2 & 4 & 6 & 5 & 2 \\
\hline
\end{array}
\][/tex]
