Question

The random variable X is a binomial random variable with n=17 and p=0.2 . What is the standard deviation of X? Round your answer to two decimal places.

Answer 1

The standard deviation of the binomial random variable X with parameters n=17 and p=0.2 is approximately 1.65 when rounded to two decimal places.

The standard deviation (\(\sigma\)) of a binomial distribution is given by the formula:

`\[ \sigma = √(n * p * (1 - p)) \]`

Given that n = 17 and p = 0.2, substitute these values into the formula:

`\[ \sigma = √(17 * 0.2 * (1 - 0.2)) \]`

Calculate the expression to find the standard deviation. Round the result to two decimal places.

`\[ \sigma = √(17 * 0.2 * (1 - 0.2)) \]\[ \sigma = √(17 * 0.2 * 0.8) \]\[ \sigma = √(2.72) \]\[ \sigma \approx 1.65 \]`

Therefore, the standard deviation of the binomial random variable \(X\) with n = 17 and p = 0.2 is approximately 1.65 (rounded to two decimal places).