Probability Distributions — Important Questions

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.

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.

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.

2.4

For binomial distribution, Variance = npq = 10 × 0.4 × 0.6 = 2.4. Here q = 1 - p = 1 - 0.4 = 0.6.