Question

Find the following binomial probabilities:

a. n= 8 , p = .25 , p (x=4)

b. n= 16 , p= .4 , P ( 4 ≤ X ≤7)

c. n=11 , p = .5 , P ( x > 8)

Answer 1

The binomial distribution is used to calculate probabilities in scenarios with a fixed number of trials and two possible outcomes. We can use the binomial probability formula to solve each part of the question.

Step-by-step explanation:

The binomial distribution is used to calculate probabilities in scenarios with a fixed number of trials and two possible outcomes. Let's solve each part of the question:

a. n = 8, p = .25, p(x=4):

1. Calculate the binomial probability using the formula: P(x) = C(n, x) * p^x * (1-p)^(n-x)
2. Substitute the values into the formula: P(4) = C(8, 4) * 0.25^4 * (1-0.25)^(8-4)
3. Calculate the result: P(4) ≈ 0.0571

b. n = 16, p = .4, P(4 ≤ X ≤ 7):

1. Calculate the binomial probabilities for X = 4, 5, 6, and 7 using the same formula
2. Add these probabilities together: P(4 ≤ X ≤ 7) = P(4) + P(5) + P(6) + P(7)
3. Calculate the result: P(4 ≤ X ≤ 7) ≈ 0.7087

c. n = 11, p = .5, P(X > 8):

1. Calculate the binomial probabilities for X = 9, 10, and 11 using the formula
2. Add these probabilities together: P(X > 8) = P(9) + P(10) + P(11)
3. Calculate the result: P(X > 8) ≈ 0.0547