Questions: A binomial experiment with probability of success p=0.61 and n=6 trials is conducted. What is the probability that the experiment results in more than 4 successes? Do not round your intermediate computations, and round your answer to three decimal places. (If necessary, consult a list of formulas.)

A binomial experiment with probability of success p=0.61 and n=6 trials is conducted. What is the probability that the experiment results in more than 4 successes?
Do not round your intermediate computations, and round your answer to three decimal places. (If necessary, consult a list of formulas.)

Transcript text: A binomial experiment with probability of success $p=0.61$ and $n=6$ trials is conducted. What is the probability that the experiment results in more than 4 successes? Do not round your intermediate computations, and round your answer to three decimal places. (If necessary, consult a list of formulas.) $\square$

Solution

Solution Steps

Step 1: Define the Problem

We are conducting a binomial experiment with $ n = 6 $ trials and a probability of success $ p = 0.61 $. We need to find the probability of obtaining more than 4 successes.

Step 2: Calculate the Probability of 4 or Fewer Successes

To find the probability of more than 4 successes, we first calculate the cumulative probability of obtaining 4 or fewer successes, denoted as $ P(X \leq 4) $. The computed value is:

\[ P(X \leq 4) \approx 0.7508 \]

Step 3: Calculate the Probability of More Than 4 Successes

The probability of obtaining more than 4 successes, denoted as $ P(X > 4) $, can be calculated using the complement of the cumulative probability:

\[ P(X > 4) = 1 - P(X \leq 4) \approx 1 - 0.7508 = 0.2492 \]

Rounding this value to three decimal places gives:

\[ P(X > 4) \approx 0.249 \]