Praxis Core Academic Skills for Educators: Mathematics (5733)Statistics and ProbabilityEasy
A quality control technician is inspecting a batch of 50 newly manufactured circuit boards. Historical data indicates that the probability of a single circuit board being defective is 0.04. Assuming each board's defect status is independent, what is the expected number of defective circuit boards in this batch?
- A5
- B2
- C1
- D4
Show answer & explanationAnswer & explanation
Correct answer: B. 2
The expected number of events in a series of independent trials is calculated by multiplying the number of trials by the probability of the event occurring in a single trial. In this case, 50 boards * 0.04 probability = 2 expected defective boards.
Why the other options are wrong
- A. Incorrect. This would be the result if the probability was 0.10.
- C. Incorrect. This would be the result if the probability was 0.02.
- D. Incorrect. This would be the result if the probability was 0.08.
Expected Value (Discrete)
The expected value of a discrete random variable is the sum of the products of each possible value of the variable and its probability.
- For a binomial distribution, E(X) = n*p, where n is the number of trials and p is the probability of success.
- Represents the long-run average outcome if the experiment were repeated many times.
- It does not have to be a value that the random variable can actually take.
Memory trick: Expect the 'N' trials to 'P'roduce results.