Question

1) Binomial distribution, f(x) = px (1 – p) n-x , x = 0, 1, 2, …, n n = 10, p = 0.5, find Probabilities a) P(X ≥ 2) b) P(X ≤ 9)

2) f(x) = (2x + 1)/25, x = 0, 1, 2, 3, 4 a) P(X = 4) b) P(X ≥ 2) c) P(X ≥ -3)

3) Z has std normal distribution, find z a) P(-1.24 < Z < z) = 0.8 b) P(-z < Z < z) = 0.9973

4) X ~ N(10, 4), find probabilities, or x a) P(-2 < X < 8) b) P(X > x) = 0.95 c) P(-x < X-5 < x) = 0.99

5)A diameter X of the dot products is normally distributed, X ~ N(0.002, 0.0042 ). a) What is the probability that diameter of a dot exceed 0.0026? b) What is the probability that diameter is between 0.0014 and 0.0026? c) What standard deviation of diameters is needed so that the probability in part (b) is 0.995?

6) RV X ~ N(10, σ2 ), find σ to meet a. P (X < 6) = 0.1245 b. P (X > 13) = 0.2562

Answer 1