Practice Test GeeksAP Practice Test
← All AP Flashcard Decks

Probability and Distributions Flashcards

7 cards from real AP 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 and Distributions flashcards as text

  1. A binomial random variable has n = 20 and p = 0.4. What is its standard deviation?

    Answer: 2.19

    σ = √(np(1−p)) = √(20 × 0.4 × 0.6) = √4.8 ≈ 2.19.

  2. Using the standard normal table, approximately what proportion of data falls within one standard deviation of the mean?

    Answer: 68%

    The empirical rule states that approximately 68% of data lies within ±1σ of the mean in a normal distribution.

  3. A student randomly guesses on a 10-question true/false test. What is the probability of getting exactly 7 correct?

    Answer: 0.117

    P(X = 7) = C(10,7)(0.5)^7(0.5)^3 = 120 × (1/1024) ≈ 0.117.

  4. If X ~ N(100, 15²), what is P(X > 130) using the empirical rule?

    Answer: Approximately 2.5%

    130 is 2σ above the mean; 95% falls within ±2σ, so 2.5% lies above 130.

  5. The variance of a discrete random variable X is defined as:

    Answer: E[(X − μ)²]

    Variance is the expected value of the squared deviation from the mean: σ² = E[(X − μ)²].

  6. Two independent random variables X and Y have variances 9 and 16 respectively. What is Var(X + Y)?

    Answer: 25

    For independent variables, Var(X + Y) = Var(X) + Var(Y) = 9 + 16 = 25.

  7. A Poisson random variable models the number of emails received per hour with mean λ = 3. What is P(X = 0)?

    Answer: e⁻³ ≈ 0.050

    P(X = 0) = e^(−λ)λ^0/0! = e^(−3) ≈ 0.050.