Question

# Eighty dash four percent of adults in a certain country believe that life on other planets...

Eighty dash four 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. ​(Round to two decimal places as​ needed.)

Find the variance of the binomial distribution. nothing ​(Round to two decimal places as​ needed.)

Find the standard deviation of the binomial distribution. ​(Round to two decimal places as​ needed.) Interpret the results. On​ average, nothing out of every 5 adults in the country believe that life on other planets is plausible. In most samples of 5​ adults, the number of adults who think life on other planets is plausible would differ from the mean by no more than nothing. ​(Type integers or decimals rounded to two decimal places as​ needed.)

Solution :

Given that,

p = 84% = 0.84

q = 1 - p = 1 - 0.84 = 0.16

n = 5

here X~binomial(n=5,p=0.84)

Uisng binomial distribution,

mean = n * p = 5 * 0.84= 4.2

variance = n * p *q = 5 * 0.84 * 0.16 = 0.67

standard deviation = variance = 0.67 = 0.82

#On​ average, 4.2 out of every 5 adults in the country believe that life on other planets is plausible. In most samples of 5​ adults, the number of adults who think life on other planets is plausible would differ from the mean by no more than 0.82