Probability & Statistics Flashcards
7 cards from real BSIE practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Probability & Statistics flashcards as text
In hypothesis testing, a Type II error occurs when you:
Answer: Fail to reject a false null hypothesis
A Type II error (β) is failing to reject H₀ when H₀ is actually false — missing a real effect.
A 95% confidence interval for a population mean is calculated as (47.2, 52.8). What is the sample mean?
Answer: 50.0
The sample mean is the midpoint of the confidence interval: (47.2 + 52.8) / 2 = 50.0.
Which probability rule states P(A ∩ B) = P(A) × P(B) when A and B are independent?
Answer: Multiplication rule
The multiplication rule for independent events states that the joint probability equals the product of the individual probabilities.
For a right-skewed distribution, which inequality is typically true?
Answer: Mean > Median > Mode
In a right-skewed distribution, the long right tail pulls the mean above the median, which is above the mode.
A random variable X has E[X] = 10 and Var(X) = 4. What is E[3X + 5]?
Answer: 35
E[3X + 5] = 3·E[X] + 5 = 3(10) + 5 = 35.
In statistical process control, a control chart signals a process is out of control when:
Answer: A point falls beyond 3 standard deviations from the centerline
Points beyond ±3σ (3 standard deviations) from the centerline are the standard signal of an out-of-control process.
The geometric distribution models:
Answer: Number of trials until the first success
The geometric distribution gives the probability that the first success occurs on the k-th trial in a sequence of Bernoulli trials.