The number of prescriptions filled at a pharmacy each hour during an 8-hour period is shown in the table. The employee spilled coffee on the table, making the entry for hour 2 unreadable. The employee knows that the mean for the data in the table is 21. How many prescriptions were filled during hour 2?
| Hour | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Number of Prescriptions | 18 | ? | 22 | 25 | 16 | 24 | 22 | 28 |
A. 13
B. 14
C. 20
D. 22
Answer (1)
Let x be the number of prescriptions filled during hour 2.
Set up the equation for the mean: 8 18 + x + 22 + 25 + 16 + 24 + 22 + 28 = 21 .
Simplify the equation to x + 155 = 168 .
Solve for x : x = 13 . The number of prescriptions filled during hour 2 is 13 .
Explanation
Understanding the Problem We are given the number of prescriptions filled at a pharmacy for 8 hours, but the number for hour 2 is missing. We know the mean number of prescriptions filled per hour is 21. Our goal is to find the number of prescriptions filled during hour 2.
Setting up the Equation Let x be the number of prescriptions filled during hour 2. The mean of the 8 hours is calculated as the sum of prescriptions divided by 8. So, we have the equation: 8 18 + x + 22 + 25 + 16 + 24 + 22 + 28 = 21
Multiplying by 8 Multiply both sides of the equation by 8 to get rid of the fraction: 18 + x + 22 + 25 + 16 + 24 + 22 + 28 = 21 × 8 We calculated that 21 × 8 = 168 .
Simplifying the Equation Now, simplify the left side of the equation by adding the known numbers: 18 + 22 + 25 + 16 + 24 + 22 + 28 = 155 So the equation becomes: x + 155 = 168
Solving for x To solve for x , subtract 155 from both sides of the equation: x = 168 − 155 We calculated that 168 − 155 = 13 .
Final Answer Therefore, the number of prescriptions filled during hour 2 is 13.
Examples
Understanding mean values is crucial in many real-world scenarios. For instance, if you're tracking your spending over a month, calculating the mean daily expenditure can help you budget effectively. Similarly, in sports, a basketball player's average points per game gives an idea of their performance consistency. In environmental science, the average rainfall in a region helps in planning water resources. These examples show how the concept of the mean is a fundamental tool for analysis and decision-making in various fields.
