Enter your answer and show all the steps that you use to solve this problem in the space provided.Use the binomial expression (p+q)n to calculate a binomial distribution with n = 5 and p = 0.3.
To calculate a binomial distribution with n = 5 and p = 0.3, we can use the formula:
P(X=k) = (n choose k) * p^k * q^(n-k)
where
n = 5
p = 0.3
q = 1 - p = 0.7
For k = 0:
P(X=0) = (5 choose 0) * 0.3^0 * 0.7^5
P(X=0) = 1 * 1 * 0.16807
P(X=0) = 0.16807
For k = 1:
P(X=1) = (5 choose 1) * 0.3^1 * 0.7^4
P(X=1) = 5 * 0.3 * 0.2401
P(X=1) = 0.36015
For k = 2:
P(X=2) = (5 choose 2) * 0.3^2 * 0.7^3
P(X=2) = 10 * 0.09 * 0.343
P(X=2) = 0.3087
For k = 3:
P(X=3) = (5 choose 3) * 0.3^3 * 0.7^2
P(X=3) = 10 * 0.027 * 0.49
P(X=3) = 0.1323
For k = 4:
P(X=4) = (5 choose 4) * 0.3^4 * 0.7^1
P(X=4) = 5 * 0.081 * 0.7
P(X=4) = 0.2835
For k = 5:
P(X=5) = (5 choose 5) * 0.3^5 * 0.7^0
P(X=5) = 1 * 0.243 * 1
P(X=5) = 0.243
Therefore, the binomial distribution with n = 5 and p = 0.3 is:
P(X=0) = 0.16807
P(X=1) = 0.36015
P(X=2) = 0.3087
P(X=3) = 0.1323
P(X=4) = 0.2835
P(X=5) = 0.243