Practice Test Geeks(NBT) National Benchmark Test Practice Test
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NBT Statistics and Probability Flashcards

6 cards from real NBT practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 6 NBT Statistics and Probability flashcards as text

  1. A dataset has mean μ = 50 and standard deviation σ = 10. A new value of 80 is added to the dataset of 99 values. Which statement best describes the effect on the standard deviation?

    Answer: The standard deviation will increase because 80 is far from the mean

    Adding a value that is far from the current mean (80 is 3 standard deviations above μ = 50) increases the spread of the data, which increases the standard deviation. The new value pulls the mean slightly upward and contributes a large squared deviation, raising the overall variance and thus the standard deviation.

  2. Events A and B satisfy P(A) = 0.5, P(B) = 0.4, and P(A ∪ B) = 0.7. What is P(A | B)?

    Answer: 0.5

    Using the addition rule: P(A ∩ B) = P(A) + P(B) − P(A ∪ B) = 0.5 + 0.4 − 0.7 = 0.2. Then P(A | B) = P(A ∩ B) / P(B) = 0.2 / 0.4 = 0.5. Note that P(A | B) = P(A) = 0.5, which means A and B are actually independent events.

  3. A box contains 4 red and 6 blue marbles. Two marbles are drawn without replacement. Given that the second marble drawn is red, what is the probability that the first marble drawn was also red?

    Answer: 1/3

    Using Bayes' theorem: P(1st red | 2nd red) = P(2nd red | 1st red) × P(1st red) / P(2nd red). P(1st red) = 4/10. P(2nd red | 1st red) = 3/9. P(2nd red | 1st blue) = 4/9. P(2nd red) = (4/10)(3/9) + (6/10)(4/9) = 12/90 + 24/90 = 36/90 = 2/5. So P(1st red | 2nd red) = (3/9 × 4/10) / (2/5) = (12/90) / (36/90) = 12/36 = 1/3.

  4. The scores on an NBT test are normally distributed with mean 520 and standard deviation 80. If the top 16% of students receive a distinction, approximately what is the minimum score needed for a distinction?

    Answer: 600

    In a normal distribution, approximately 84% of values lie below μ + σ, meaning approximately 16% lie above μ + σ. Here μ + σ = 520 + 80 = 600. So a student needs a score of at least 600 to be in the top 16%.

  5. A fair six-sided die is rolled 4 times. What is the probability of getting an even number on exactly 3 of the 4 rolls?

    Answer: 1/4

    Each roll has P(even) = 1/2. Using the binomial formula: P(X = 3) = C(4,3) × (1/2)³ × (1/2)¹ = 4 × (1/8) × (1/2) = 4/16 = 1/4. Note that two answer choices show 1/4 — the correct reasoning uses the binomial distribution with n=4, k=3, p=1/2.

  6. Two variables X and Y have a correlation coefficient of r = −0.85. A researcher concludes: 'Since r is close to −1, increasing X causes Y to decrease.' Which criticism of this conclusion is most statistically valid?

    Answer: Correlation measures linear association strength and direction but does not establish causation

    Correlation coefficients (r) measure the strength and direction of a linear relationship between two variables, but they do not imply causation. Even a strong correlation like r = −0.85 could result from a lurking variable, reverse causation, or coincidence. Claiming that X 'causes' Y to decrease is a logical fallacy known as confusing correlation with causation.