Subjects statistics

Percentile Wait Time 20D221

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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.