Question

work and ask uiem wneier uiey uiane oversieeping. ine iandoni vaiiabe represents uie numoer or u.s. employees wno are iate ior work and blame oversleeping.
find the mean of the binomial distribution.
μ = 0.36 (round to the nearest hundredth as needed.)
find the variance of the binomial distribution.
σ² = 0.33 (round to the nearest hundredth as needed.)
find the standard deviation of the binomial distribution.
σ = 0.36 (round to the nearest hundredth as needed.)

Explanation:

To find the standard deviation of a binomial distribution, we use the formula for the standard deviation of a binomial distribution, which is the square root of the variance.

Step 1: Recall the formula for standard deviation of a binomial distribution

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

Step 2: Substitute the given variance into the formula

We are given that the variance \(\sigma^{2} = 0.33\). So we need to calculate \(\sqrt{0.33}\).

Step 3: Calculate the square root

\(\sqrt{0.33}\approx0.57\) (rounded to the nearest hundredth).

Answer:

The standard deviation of the binomial distribution is approximately \(\boldsymbol{0.57}\).