Question

find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n = 70, p = 0.4 the mean, \\( \mu \\), is 28.0. (round to the nearest tenth as needed.) the variance, \\( \sigma ^ { 2 } \\), is 16.8. (round to the nearest tenth as needed.) the standard deviation, \\( \sigma \\), is \\( \square \\). (round to the nearest tenth as needed.)

Explanation:

Step1: Recall the formula for standard deviation

The standard deviation \(\sigma\) of a binomial distribution is \(\sigma=\sqrt{\sigma^{2}}\), where \(\sigma^{2}\) is the variance.

Step2: Substitute the value of variance

Given \(\sigma^{2} = 16.8\), then \(\sigma=\sqrt{16.8}\).

Step3: Calculate the square - root

Using a calculator, \(\sqrt{16.8}\approx4.1\)

Answer:

\(4.1\)