To solve the problem of finding the number of prescriptions filled during hour 2, we need to follow several steps. Given that the mean number of prescriptions filled over an 8-hour period is 21, we will use this information to determine the missing value.
Given data:
- Number of prescriptions over the 8 hours (with one missing value): [18, ?, 22, 25, 16, 24, 22, 28]
- Mean of the prescriptions over 8 hours: 21
Let's break down the steps:
1. Calculate the total number of prescriptions:
Since the mean number of prescriptions is 21, and there are 8 hours, the total number of prescriptions over the 8 hours can be calculated as:
[tex]\[
\text{Total Prescriptions} = \text{Mean Prescriptions} \times \text{Number of Hours} = 21 \times 8 = 168
\][/tex]
2. Sum the known prescriptions:
From the table, we have the following prescriptions filled for each hour (excluding the unreadable hour 2):
- Hour 1: 18
- Hour 2: ?
- Hour 3: 22
- Hour 4: 25
- Hour 5: 16
- Hour 6: 24
- Hour 7: 22
- Hour 8: 28
Adding these known values:
[tex]\[
18 + 22 + 25 + 16 + 24 + 22 + 28 = 155
\][/tex]
3. Determine the missing value:
Let [tex]\( ? \)[/tex] represent the unknown number of prescriptions for hour 2. We have the total number of prescriptions over 8 hours as 168, and we know the sum of the known prescriptions is 155. To find the missing value, we can set up the equation:
[tex]\[
\text{Missing Prescription} = \text{Total Prescriptions} - \text{Sum of Known Prescriptions}
\][/tex]
Substituting the known values:
[tex]\[
\text{Missing Prescription} = 168 - 155 = 13
\][/tex]
Therefore, the number of prescriptions filled during hour 2 is 13.
