Question

In Exercises \(\mathrm{P} .112\) to \(\mathrm{P} .115,\) calculate the mean and standard deviation of the binomial random variable. A binomial random variable with \(n=6\) and \(p=0.4\)

Short answer

The mean of the binomial distribution is 2.4 and the standard deviation is approximately 1.2

Step-by-step solution

Compute the mean

The mean (expected value) of a binomial distribution can be calculated using the formula: \( \mu = np \). Substitute values into the formula: \( \mu = 6 * 0.4 = 2.4 \)

Compute the Standard Deviation

The standard deviation (σ) of a binomial distribution is calculated using the formula: \( \sigma = \sqrt{npq} \). Here, q is the probability of failure and can be calculated as \( q = 1 - p \). Thus, we'll have: \( \sigma = \sqrt{6*0.4*0.6} \)