The distribution of the binomial random variable (X) has the following parameters p = 0.3 and n = 9. Determinep (1 less or equal to X less or equal to 4).
A)0.7052
B)0.9060
C)0.7715
D)0.8550
E)0.6255
To determine P(1 ≤ X ≤ 4), we need to calculate the cumulative probability from X = 1 to X = 4.
First, we calculate P(X = 0):
P(X = 0) = (9 choose 0) * (0.3)^0 * (0.7)^9 = 0.7^9 ≈ 0.0028
Next, we calculate P(X = 1):
P(X = 1) = (9 choose 1) * (0.3)^1 * (0.7)^8 = 0.3 * 0.7^8 ≈ 0.0286
Next, we calculate P(X = 2):
P(X = 2) = (9 choose 2) * (0.3)^2 * (0.7)^7 = 0.0433
Next, we calculate P(X = 3):
P(X = 3) = (9 choose 3) * (0.3)^3 * (0.7)^6 = 0.0984
Next, we calculate P(X = 4):
P(X = 4) = (9 choose 4) * (0.3)^4 * (0.7)^5 = 0.1211
Now, we sum all these probabilities to get P(1 ≤ X ≤ 4):
P(1 ≤ X ≤ 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
P(1 ≤ X ≤ 4) = 0.0286 + 0.0433 + 0.0984 + 0.1211
P(1 ≤ X ≤ 4) ≈ 0.2914
Therefore, none of the given options match the calculated answer.