Question

seventy - two percent of adults in a certain country believe that life on other planets is plausible. you randomly select five adults and ask them whether they believe that life on other planets is plausible. the random variable represents the number of adults who believe that life on other planets is plausible. find the mean, variance, and standard deviation of the binomial distribution for the random variable. interpret the results.
find the mean of the binomial distribution.
\\( \mu=3.6 \\) (round to two decimal places as needed.)
find the variance of the binomial distribution.
\\( \sigma^{2}=1.01 \\) (round to two decimal places as needed.)
find the standard deviation of the binomial distribution.
\\( \sigma=\square \\) (round to two decimal places as needed.)

Explanation:

Step1: Recall the formula for standard deviation of binomial distribution

The formula for standard deviation of binomial distribution is $\sigma=\sqrt{\sigma^{2}}$.

Step2: Substitute the value of variance

Given $\sigma^{2} = 1.01$, then $\sigma=\sqrt{1.01}$.

Step3: Calculate the value

Using a calculator, $\sqrt{1.01}\approx1.00$ (rounded to two decimal places).

Answer:

$1.00$