To determine how many prescriptions were filled during hour 2, we are given that the mean (average) number of prescriptions filled over 8 hours is 21. Here's a detailed, step-by-step solution to find the missing value:
1. Understand the Given Data:
- Mean of prescriptions filled over 8 hours = 21
- Number of prescriptions filled in 7 of those hours: 18, \(?\) (unknown), 22, 25, 16, 24, 22, 28
2. Calculate the Total Sum of Prescriptions:
Since the mean of the prescriptions filled is 21 over 8 hours, we can calculate the total sum of prescriptions filled by multiplying the mean by the number of hours:
[tex]\[
\text{Total Sum} = \text{Mean} \times \text{Number of Hours} = 21 \times 8 = 168
\][/tex]
3. Sum of Known Values:
Next, we need to sum the known number of prescriptions filled during the 7 hours that we have data for:
[tex]\[
18 + 22 + 25 + 16 + 24 + 22 + 28 = 155
\][/tex]
4. Find the Missing Value:
To find the missing value (number of prescriptions filled during hour 2), we subtract the sum of the known values from the total sum:
[tex]\[
\text{Missing Value} = \text{Total Sum} - \text{Sum of Known Values} = 168 - 155 = 13
\][/tex]
Therefore, the number of prescriptions filled during hour 2 is \( 13 \).
Hence, the correct answer is:
A. 13
