A security system has a failure rate of 2%. If there are 500 systems installed,

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Question: A security system has a failure rate of 2%. If there are 500 systems installed, how many are expected to fail?

Options:

Correct Answer: 10

Solution:

Expected failures = 2% of 500 = 0.02 * 500 = 10 systems.

A security system has a failure rate of 2%. If there are 500 systems installed, how many are expected to fail?

A security system has a failure rate of 2%. If there are 500 systems installed, how many are expected to fail?

Step 1: Understand that the failure rate of the security system is 2%.
Step 2: Convert the percentage into a decimal. 2% as a decimal is 0.02.
Step 3: Identify the total number of systems installed, which is 500.
Step 4: Calculate the expected number of failures by multiplying the failure rate (0.02) by the total number of systems (500).
Step 5: Perform the multiplication: 0.02 * 500 = 10.
Step 6: Conclude that the expected number of systems that will fail is 10.

Probability and Statistics – Understanding failure rates and how to calculate expected outcomes based on percentages.
Basic Arithmetic – Performing multiplication to find the expected number of failures.