Praxis Core Academic Skills for Educators: Mathematics (5733)Statistics and ProbabilityEasy
A manufacturing plant produces light bulbs. Historical data shows that 3% of the bulbs produced are defective. If a quality control inspector randomly selects 100 bulbs, what is the expected number of defective bulbs?
- A5
- B3
- C1
- D10
Show answer & explanationAnswer & explanation
Correct answer: B. 3
The expected number of defective bulbs is calculated by multiplying the total number of bulbs selected by the probability of a bulb being defective. Expected Value = n * p = 100 * 0.03 = 3.
Why the other options are wrong
- A. Incorrect calculation.
- C. Incorrect calculation; perhaps a misinterpretation of percentage.
- D. Incorrect calculation; this would be if the defect rate was 10%.
Expected Value (Discrete)
The average outcome of a random variable over a large number of trials, calculated as the sum of (each outcome * its probability).
- For n trials with probability p, E(X) = n * p.
- Represents the long-run average.
- Does not guarantee that outcome will occur in a single trial.
Memory trick: Expected value: what you 'expect' on average, probability times trials.