Question

For a binomial experiment with n= 12 trials and probability of success p = 0.64,

Find the probability of 9 successes out of 12 trials, P(9).

Find the probability of less than 3 successes out of 12 trials, P(x < 3). (Hint: don't forget that 0 successes is an option!)

Find the probability of 3 or more successes out of 12 trials, P(x ≥ 3). (Hint: Try the complement rule!)

Find the mean of the given binomial probability distribution. Find the standard deviation of the given binomial probability distribution.

Answer 1

To find P(9), use the binomial probability formula. To find P(x < 3) and P(x ≥ 3), calculate the probabilities of 0, 1, 2 successes. The mean of the binomial distribution is np, and the standard deviation is √(npq).

Step-by-step explanation:

Probability of 9 successes out of 12 trials:

The probability of getting 9 successes out of 12 trials can be calculated using the binomial probability formula. P(9) = C(12,9) * (0.64)^9 * (1-0.64)^(12-9).

Probability of less than 3 successes out of 12 trials:

To find P(x < 3), we need to calculate the probabilities of getting 0, 1, and 2 successes out of 12 trials and sum them up. P(x < 3) = P(0) + P(1) + P(2).

Probability of 3 or more successes out of 12 trials:

To find P(x ≥ 3), we can use the complement rule. P(x ≥ 3) = 1 - P(x < 3).

Mean of the binomial distribution:

The mean of a binomial distribution is given by µ = np. In this case, µ = 12 * 0.64.

Standard deviation of the binomial distribution:

The standard deviation of a binomial distribution is given by σ = √(npq). In this case, σ = √(12 * 0.64 * (1 - 0.64)).