Solve for the probabilities of the following binomial distribution problems by u

Question

Solve for the probabilities of the following binomial distribution problems by using the binomial formula. a. If n = 11 and p = 23, what is the probability that x = 4? b. If n = 6 and p = 50, what is the probability that x greaterthanorequalto 1? c. If n = 9 and p = 85, what is the probability that x > 7? d. If n = 14 and p = 70, what is the probability that x lessthanorequalto 3? (Round your answers to 4 decimal places.) a. P(x = 4 | n = 11 and p = 23) = b. P(x greaterthanorequalto 1 | n = 6 and p = 50) = c. P(x > 7 | n = 9 and p = 85) = d. P(x lessthanorequalto 3 | n = 14 and p = 70) =

Explanation / Answer

(A)
P(x=4 | n=11 and p=0.23) = 11C4 * 0.23^4 * (1-0.23)^7 = 0.1482

(B)
P(x>=1 | n=6 and p =0.50) = 1 - 6C0 * 0.5^0 * (1-0.5)^6 = 0.9844

(C)
P(x>7 | n=9 and p=0.85) = 9C8 * 0.85^8 * (1-0.85)^1 + 9C9 * 0.85^9 * (1-0.85)^0 = 0.5995

(D)
P(x<=3 | n=14 and p=0.7) = 14C0 * 0.7^0 * (1-0.7)^14 + 14C1 * 0.7^1 * (1-0.7)^13 + 14C2 * 0.7^2 * (1-0.7)^12 + 14C3 * 0.7^3 * (1-0.7)^11 = 0.0002465

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