Question

Assume that a procedure yields a binomial distribution with n=297
trials and the probability of success for one trial is p=37%

find the standard deviation for this distribution
.

Answer 1

The standard deviation for a binomial distribution can be found using the formula:

σ = √(n * p * (1 - p))

where:
- σ is the standard deviation
- n is the number of trials (n = 297 in your case)
- p is the probability of success on an individual trial (p = 0.37 in your case)

Plugging these values into the formula, we get:

σ = √(297 * 0.37 * (1 - 0.37))
σ = √(109.89 * 0.63)
σ = √(69.2307)

Calculating the square root of 69.2307 gives us:

σ ≈ 8.319

Therefore, the standard deviation for this binomial distribution is approximately 8.319.