Question

Find the​ mean, variance, and standard deviation of the binomial distribution with the given values of n and p. ​, The​ mean, ​, is nothing. ​(Round to the nearest tenth as​ needed.)

Answer 1

Complete Question

Find the​ mean, variance, and standard deviation of the binomial distribution with the given values of n and p. ​, The​ mean, ​, is nothing. ​(Round to the nearest tenth as​ needed.)

    p =  0.6   n =  18

Answer:

The mean   $\mu = 10.5$

The standard deviation $\sigma = 2.08$

The  variance   $var = 4.32$

Step-by-step explanation:

From the question we are told that

      The probability of success   is  $p = 0.6$

      The  sample size is $n = 18$

  Generally given that the distribution is binomial, then the probability of failure is mathematically represented as

              $q = 1- p$

substituting values

              $q = 1- 0.6$

              $q =0.4$

Generally the mean is mathematically evaluated as

             $\mu = np$

substituting values

             $\mu = 18 * 0.6$    

             $\mu = 10.5$

The  standard deviation is evaluated as

              $\sigma = \sqrt{npq}$

substituting values

               $\sigma = \sqrt{18 * 0.6 * 0.4}$

              $\sigma = 2.08$

The variance is evaluated as

               $var = \sigma^2$

substituting value

              $var = 2.08^2$

              $var = 4.32$