Question

Sixty-nine 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.

Answer 1

Solution :

Given that,

p = 69% = 0.69

q = 1 - p = 1 - 0.69 = 0.31

n = 5

Uisng binomial distribution,

mean = n * p = 5 * 0.69 = 3.45

variance = n * p *q = 5 * 0.69 * 0.31 = 1.0695

standard deviation = $\sqrt$ variance = $\sqrt$ 1.0695 = 1.0342