Question

the data set represents wait times (in minutes) for various services at a states department of motor vehicles locations. find the percentile that corresponds to a wait time of 4 minutes.27 4 8 4 3 26 18 21 1 3 3 5 5 6 10 122 23 10 6 7 2 1 6 6 2 4 14 15 16 4 193 19 26 5 3 4 7 6 10 9 10 20 18 3 20 10a wait time of 4 minutes corresponds to about a percentile of (round to the nearest whole number as needed.)

Explanation:

Step1: Count total data points

Count all values: there are 45 data points, so $n=45$.

Step2: Sort data in ascending order

Sorted data: $1,1,1,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,7,7,8,9,10,10,10,10,10,14,15,16,18,18,19,19,20,20,21,22,26,26,27$

Step3: Count values ≤ 4

Count numbers less than or equal to 4: there are 15 values.

Step4: Calculate percentile

Use percentile formula: $\text{Percentile} = \frac{\text{Number of values } \leq 4}{n} \times 100$
$\text{Percentile} = \frac{15}{45} \times 100 \approx 33.33$

Step5: Round to nearest whole number

Round $33.33$ to the nearest integer.

Answer:

33