A warehouse worker fills 150 orders per day on average. From day to day, the number of orders varies by 2%. What is the range of the number of orders the worker fills each day?
Understand the Problem
The question is asking us to calculate the range of orders filled by a warehouse worker who averages 150 orders per day, taking into account a variation of 2% in the number of orders from day to day.
Answer
The range of orders filled each day is $[147, 153]$.
Answer for screen readers
The range of the number of orders the worker fills each day is from 147 to 153.
Steps to Solve
- Calculate 2% of the Average Orders
First, we need to find 2% of the average number of orders, which is 150.
To find 2%, we multiply 150 by 0.02:
$$ 2% \text{ of } 150 = 150 \times 0.02 = 3 $$
- Determine the Minimum Orders
Now we calculate the minimum number of orders filled by subtracting the 2% variation from the average:
$$ \text{Minimum Orders} = 150 - 3 = 147 $$
- Determine the Maximum Orders
Next, we calculate the maximum number of orders filled by adding the 2% variation to the average:
$$ \text{Maximum Orders} = 150 + 3 = 153 $$
- State the Range of Orders
The range of the number of orders filled by the warehouse worker is given by the minimum and maximum values calculated:
$$ \text{Range} = [147, 153] $$
The range of the number of orders the worker fills each day is from 147 to 153.
More Information
This range indicates the variability in daily order fulfillment based on a 2% fluctuation, which shows that while the average remains 150, actual performance can differ.
Tips
- Miscalculating the percentage: Always remember to convert the percentage to a decimal (2% = 0.02) before performing multiplication.
- Forgetting to add and subtract from the average: Ensure both calculations for minimum and maximum orders are completed to find the complete range.
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