An employee records the number of prescriptions filled at a pharmacy each hour during an 8-hour period. The table shows the results.
Number of Prescriptions Filled at a Pharmacy
| Hour | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Number of Prescriptions | 18 | ? | 22 | 25 | 16 | 24 | 22 | 28 |
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?
A. 13
B. 14
C. 20
D. 22
Answer (2)
Let x represent 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 .
Solve for x : 18 + x + 22 + 25 + 16 + 24 + 22 + 28 = 168 , which simplifies to 155 + x = 168 .
Find the value of x : x = 168 − 155 = 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 are also given that the mean number of prescriptions filled during the 8-hour period 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 number of prescriptions filled during the 8-hour period is calculated by summing the number of prescriptions filled each hour and dividing by the number of hours, which is 8. So, we have the equation: 8 18 + x + 22 + 25 + 16 + 24 + 22 + 28 = 21
Multiplying by 8 To solve for x , we first multiply both sides of the equation by 8: 18 + x + 22 + 25 + 16 + 24 + 22 + 28 = 21 × 8 18 + x + 22 + 25 + 16 + 24 + 22 + 28 = 168
Simplifying the Equation Next, we simplify the left side of the equation by adding the known numbers: 155 + x = 168
Solving for x Now, we isolate x by subtracting 155 from both sides of the equation: x = 168 − 155 x = 13
Finding the 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 helps assess their performance. In environmental science, the average rainfall in a region is vital for agricultural planning and water resource management. These examples show how the concept of the mean is a fundamental tool for analysis and decision-making in diverse fields.
The number of prescriptions filled during hour 2 is 13. This is determined by setting up an equation for the mean of the data and solving for the unknown value. Therefore, the selected answer is option A, 13.
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