Explanation
1. Understanding the Problem Logic
The problem states that a tiny percentage (0.08%) of the total items inspected are identified as defective and rejected. We need to determine the total number of inspected items required so that the absolute count of these rejected items equals exactly 2.
2. Setting Up the Algebraic Equation
Let the total number of samples that need to be inspected be x.
According to the given condition, 0.08% of this total quantity x is equal to 2:
0.08% of x=2
Convert the percentage into its fractional equivalent by dividing by 100:
1000.08×x=2
3. Solving for x
To clear the fraction, multiply both sides by 100:
0.08×x=2×100
0.08x=200
Now, isolate x by dividing by 0.08:
x=0.08200
To simplify the decimal division, eliminate the decimal point in the denominator by multiplying both the numerator and the denominator by 100:
x=8200×100
x=820000
Divide the values:
x=2500
Final Answer
The total number of samples that should be inspected is 2500.
Therefore, the correct option is (b).
