Probability Distributions — Practice Quiz
CBSE · Class 12 · Applied Mathematics
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Quick Quiz: Probability Distributions
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A fair coin is tossed 3 times. What is the probability of getting exactly 2 heads?
In a binomial distribution with n = 5 and p = 0.3, what is the mean?
A random variable X has the probability distribution: P(X=0)=0.2, P(X=1)=0.5, P(X=2)=0.3. Calculate E(X).
In a Poisson distribution with λ = 2, what is P(X = 0)?
Sample Questions
Which of the following are properties of normal distribution? (Select all correct answers)
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Bell-shaped curve, Mean = Median = Mode, Symmetric about mean, Total area under curve = 1
Normal distribution is continuous (not discrete), has a bell-shaped curve, is symmetric about the mean where mean = median = mode, and the total area under the curve equals 1.
If X ~ N(50, 25), what is the Z-score for X = 60?
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2
Z = (x - μ)/σ = (60 - 50)/5 = 10/5 = 2. Here σ = √25 = 5. The Z-score tells us that X = 60 is 2 standard deviations above the mean.
A die is rolled 4 times. What is the probability of getting exactly one '6'?
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500/1296
This is binomial with n=4, p=1/6, q=5/6. P(X=1) = ⁴C₁(1/6)¹(5/6)³ = 4 × (1/6) × (125/216) = 500/1296.
In a binomial distribution B(10, 0.4), what is the variance?
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2.4
For binomial distribution, Variance = npq = 10 × 0.4 × 0.6 = 2.4. Here q = 1 - p = 1 - 0.4 = 0.6.
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