Practice Test Geeks(TMUA) Test of Mathematics for University Admission Practice Test
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Statistics Flashcards

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

Read the first 7 Statistics flashcards as text

  1. A continuous random variable X has PDF f(x) = kx for 0 ≤ x ≤ 4, and 0 otherwise. What is the value of k?

    Answer: 1/8

    Integrating kx from 0 to 4 gives 8k = 1, so k = 1/8.

  2. Heights of a population are normally distributed with mean 170 cm and standard deviation 8 cm. What proportion of individuals are taller than 186 cm?

    Answer: 0.0228

    186 cm is 2 standard deviations above the mean; P(Z > 2) ≈ 0.0228.

  3. A hypothesis test uses H₀: μ = 100 vs H₁: μ > 100 with significance level α = 0.05. The test statistic is z = 1.60. What is the correct conclusion?

    Answer: Fail to reject H₀ because z < 1.645

    For a one-tailed test at α = 0.05, the critical value is z = 1.645; since 1.60 < 1.645, we fail to reject H₀.

  4. Which of the following correctly describes the relationship between variance and standard deviation?

    Answer: Variance = (Standard deviation)²

    By definition, variance = σ² and standard deviation σ = √(variance), so variance = (standard deviation)².

  5. A box contains 5 red, 3 blue, and 2 green balls. Two balls are drawn without replacement. What is the probability that both are red?

    Answer: 2/9

    P(both red) = (5/10)×(4/9) = 20/90 = 2/9.

  6. The regression line for predicting y from x passes through the point (x̄, ȳ). Which statement is always true?

    Answer: The regression line minimizes the sum of squared residuals

    The least-squares regression line is defined as the line that minimizes the sum of squared vertical residuals.

  7. A Poisson random variable X has mean λ = 3. What is P(X = 0)?

    Answer: e⁻³

    P(X=0) = e^(−λ) × λ⁰ / 0! = e^(−3).