Final answer:
To calculate the standard deviation of the binomial distribution with n=14 trials and p=0.13, use the formula σ = √npq. After calculations, the standard deviation is approximately 1.2578 when rounded to four decimal places.
Step-by-step explanation:
The standard deviation of a binomial distribution is calculated using the formula σ = √npq, where σ is the standard deviation, n is the number of trials, p is the probability of success on a single trial, and q is the probability of failure (q=1-p).
In this case, for a binomial experiment with n = 14 trials and a probability of success p = 0.13, the standard deviation can be found as follows:
First, calculate q:
q = 1 - p = 1 - 0.13 = 0.87
Next, calculate the standard deviation:
σ = √(14 * 0.13 * 0.87)
= √(1.582)
≈ 1.2578
Thus, the standard deviation, rounded to four decimal places, is σ ≈ 1.2578.