Question

Sixty-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

If random variable X represents the number of successes in n independent trails of the experiment. The experiment is repeated success, p remains same for each trail. Then the random variable X follows a binomial distribution with parameters n and p The probability n times (countable finite). The probability of function (PMF) of binomial distribution can be defined as, mass P(X x)= (1-p) 2-x x-0,1,2, The mean and standard deviation of the random variable X is E(X)np (d-)du= (x)PS From the given information, Let n 5 represents the number of adults that are randomly selected Let p 0.60 represents the proportion of adults in a certain country believe that life on other planet is plausible. Let the random variable Xrepresents the number of adults who believe that life planets is plausible on other Hence, the random variable X follows binomial distribution with parameters n-5 and p 0.60 The mean and standard deviation of the random variable Xis computed as follows: E(X)np -5(0.60) 3 V(X)np (1-p) -5x(0.60)x(1-0.60) 1.2 Sd (X) np (1-p) 1.2 =1.0954 Therefore, we would expect at least 3 adults who believe that life on other planets is plausible