To find P(X >= 4), we need to find the individual probabilities of X=4, X=5, X=6, X=7, X=8, and X=9 and sum them up.
Using the binomial probability formula:
P(X=k) = (n Choose k) * p^k * (1-p)^(n-k)
For k=4:
P(X=4) = (9 Choose 4) * 0.3^4 * (0.7)^5 = 0.3025
For k=5:
P(X=5) = (9 Choose 5) * 0.3^5 * (0.7)^4 = 0.1920
For k=6:
P(X=6) = (9 Choose 6) * 0.3^6 * (0.7)^3 = 0.0774
For k=7:
P(X=7) = (9 Choose 7) * 0.3^7 * (0.7)^2 = 0.0211
For k=8:
P(X=8) = (9 Choose 8) * 0.3^8 * (0.7)^1 = 0.0036
For k=9:
P(X=9) = (9 Choose 9) * 0.3^9 * (0.7)^0 = 0.0002
Summing up these probabilities:
P(X>=4) = P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9) = 0.5968
Therefore, the correct answer is not provided in the options.
The distribution of the binomial random variable (X) has the following parameters p = 0.3 and n = 9. Determine P(X greater or =4)
A)0.1715
B)0.9012
C)0.7297
D)0.4628
E)0.3
1 answer