The distribution of the binomial random variable (X) has the following parameters p = 0.3 and n = 9. Determine P(X greater or equal to 4)
A)0,0253
B)0,9012
C)0,7297
D)0,2703
E)0,7062
To find P(X greater or equal to 4) in a binomial distribution with p = 0.3 and n = 9, you need to calculate the probability of getting exactly 4, exactly 5, ..., up to 9 successes and then sum them up.
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)
Calculate each individually:
P(X = 4) = (9 choose 4) * 0.3^4 * 0.7^5 = 126 * 0.0081 * 0.16807 = 0.18038
P(X = 5) = (9 choose 5) * 0.3^5 * 0.7^4 = 126 * 0.00243 * 0.2401 = 0.07329
P(X = 6) = (9 choose 6) * 0.3^6 * 0.7^3 = 84 * 0.000729 * 0.343 = 0.01829
P(X = 7) = (9 choose 7) * 0.3^7 * 0.7^2 = 36 * 0.0002187 * 0.49 = 0.00376
P(X = 8) = (9 choose 8) * 0.3^8 * 0.7^1 = 9 * 0.0006561 * 0.7 = 0.00462
P(X = 9) = (9 choose 9) * 0.3^9 * 0.7^0 = 1 * 0.000729 * 1 = 0.00073
Adding all these probabilities up:
P(X ≥ 4) = 0.18038 + 0.07329 + 0.01829 + 0.00376 + 0.00462 + 0.00073 ≈ 0.28004
Therefore, the correct answer is not listed.