Question

find the standard deviation, $sigma$, for the binomial distribution with $n = 38$ and $p = 0.4$. round to the nearest hundredth as needed.

a. $sigma=0.61$
b. $sigma = 6.29$
c. $sigma=3.02$
d. $sigma=7.14$

Explanation:

Step1: Recall binomial std - dev formula

The formula for the standard deviation $\sigma$ of a binomial distribution is $\sigma=\sqrt{np(1 - p)}$, where $n$ is the number of trials and $p$ is the probability of success on a single - trial.

Step2: Substitute given values

Given $n = 38$ and $p=0.4$, then $1 - p=1 - 0.4 = 0.6$. Substitute these values into the formula: $\sigma=\sqrt{38\times0.4\times0.6}$.

Step3: Calculate the value inside the square - root

First, calculate $38\times0.4\times0.6=38\times0.24 = 9.12$.

Step4: Calculate the square - root

$\sigma=\sqrt{9.12}\approx3.02$.

Answer:

C. $\sigma = 3.02$