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=10 \text { and }\\\ &p=0.8 \end{aligned} $$

Short answer

The mean of the binomial random variable is 8 and the standard deviation is approximately 1.265.

Step-by-step solution

Calculate the Mean

The formula to calculate the mean (\(μ\)) of the binomial random variable is given by \(μ = n*p\). Here, we are given n=10 and p=0.8. Plug in these values into the formula to get the mean. Thus, \(μ = 10 * 0.8 = 8\).

Calculate the Standard Deviation

The formula to calculate the standard deviation (\(σ\)) of a binomial random variable is given by \(σ = \sqrt{n*p*(1-p)}\). Plug in the given values into the formula, here: n=10, p=0.8, so (1-p)=0.2. Thus, \(σ = \sqrt{10 * 0.8 * 0.2} = 1.265\). Take the square root of the result to get the standard deviation.