To find the standard deviation of the number of patients who survive out of the next 7 patients undergoing the delicate heart operation, we need to use the binomial distribution formula. The binomial distribution describes the number of successes (in this case, patients surviving) in a fixed number of independent trials (7 patients undergoing the operation), where each trial has the same probability of success (the probability of a patient surviving the operation).
The formula for the standard deviation of a binomial distribution is given by:
Standard deviation (σ) = √(n * p * q)
Where: n = Number of trials (in this case, 7 patients) p = Probability of success (in this case, the probability of a patient surviving the operation) q = Probability of failure (1 - p)
Given that the probability of a patient surviving the operation is 0.85, we can calculate q as:
q = 1 - p = 1 - 0.85 = 0.15
Now, let's calculate the standard deviation:
σ = √(7 * 0.85 * 0.15) = √(7 * 0.1275) = √(0.8925) ≈ 0.945
So, the standard deviation of the number of patients who survive out of the next 7 patients undergoing the delicate heart operation is approximately 0.945.