Question

In a binomial situation, n = 4 and π = 0.35. Find the

probabilities for all possible values of the random variable,
x. (Round your answers to 4 decimal places.)

Answer 1

To find the probabilities for all possible values of the random variable x in a binomial situation, use the binomial distribution formula. Plug in the values of n and π, and calculate the probabilities for each value of x using the formula. Round the answers to 4 decimal places.

Step-by-step explanation:

In a binomial situation, the probabilities for all possible values of the random variable x can be found using the binomial distribution formula. In this case, n = 4 and π = 0.35.

To find the probability for a specific value of x, you can use the formula:

P(x) = (nCx) * (π^x) * ((1-π)^(n-x))

Here is the probability for each possible value of x:

• P(x = 0) = (4C0) * (0.35^0) * ((1-0.35)^(4-0))
• P(x = 1) = (4C1) * (0.35^1) * ((1-0.35)^(4-1))
• P(x = 2) = (4C2) * (0.35^2) * ((1-0.35)^(4-2))
• P(x = 3) = (4C3) * (0.35^3) * ((1-0.35)^(4-3))
• P(x = 4) = (4C4) * (0.35^4) * ((1-0.35)^(4-4))

Simply calculate the values inside the brackets, raise π to the power of x, raise (1-π) to the power of (n-x), and multiply the results together to find the probabilities.

Answer 2

Using the binomial formula, calculate the probability for each possible value of x (from 0 to 4) in a binomial distribution with n = 4 and π = 0.35, rounding each result to four decimal places.

Step-by-step explanation:

In a binomial situation where n = 4 and π = 0.35, we calculate the probabilities for all possible values of the random variable, x. To do this, we use the formula for the binomial probability:

P(x) = (nCx) π^x (1-π)^(n-x)

where nCx represents the number of combinations of n items taken x at a time. We then plug in the values for x ranging from 0 to 4.

• For x = 0: P(0) = (4C0)(0.35)^0(1-0.35)^4
• For x = 1: P(1) = (4C1)(0.35)^1(1-0.35)^3
• For x = 2: P(2) = (4C2)(0.35)^2(1-0.35)^2
• For x = 3: P(3) = (4C3)(0.35)^3(1-0.35)^1
• For x = 4: P(4) = (4C4)(0.35)^4(1-0.35)^0

Each of these probabilities should be calculated and then rounded to four decimal places to get the final answers.