Question

Assume Binomial Distribution With N=10 And P=0.7. Please Show Your Answers To 4 Decimal Places.

P(X=5)=
P(X≤5)=
P(X<5)=
P(X>5)=
P(X≥5)=

Answer 1

To find the probabilities P(X=5), P(X≤5), P(X<5), P(X>5), and P(X≥5) in a binomial distribution with N=10 and P=0.7, use the binomial probability formula and calculate the respective probabilities step by step.

Step-by-step explanation:

To find the probabilities P(X=5), P(X≤5), P(X<5), P(X>5), and P(X≥5) in the given binomial distribution with N=10 and P=0.7, we can use the binomial probability formula:

P(X=k) = C(n, k) * p^k * (1-p)^(n-k)

1. Calculate P(X=5): P(X=5) = C(10, 5) * 0.7^5 * (1-0.7)^(10-5)
2. To find P(X≤5), sum up the probabilities from 0 to 5 inclusive: P(X≤5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)
3. P(X<5) is the same as P(X≤4), so we can substitute P(X=4) in the sum: P(X<5) = P(X≤4) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)
4. To find P(X>5), we can subtract P(X≤5) from 1: P(X>5) = 1 - P(X≤5)
5. P(X≥5) is the same as P(X>4), so we can substitute P(X>4) in the formula: P(X≥5) = P(X>4) = 1 - P(X≤4)