1. **State the problem:** We need to find the percentile rank corresponding to a wait time of 4 minutes in the given data set of wait times.
2. **Recall the formula for percentile rank:**
$$\text{Percentile Rank} = \frac{\text{Number of values less than } x + 0.5 \times \text{Number of values equal to } x}{\text{Total number of values}} \times 100$$
3. **List the data and count total values:**
The data set has 48 values (16 values per row, 3 rows).
4. **Count values less than 4:**
Values less than 4 are 1, 2, 3.
Count of 1's: 3
Count of 2's: 2
Count of 3's: 6
Total less than 4 = 3 + 2 + 6 = 11
5. **Count values equal to 4:**
Count of 4's: 7
6. **Apply the formula:**
$$\text{Percentile Rank} = \frac{11 + 0.5 \times 7}{48} \times 100 = \frac{11 + 3.5}{48} \times 100 = \frac{14.5}{48} \times 100$$
7. **Calculate the percentile:**
$$\frac{14.5}{48} \times 100 = 30.2083... \approx 30$$
**Final answer:** A wait time of 4 minutes corresponds to about the 30th percentile.
Percentile Wait Time 20D221
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.