Question

Suppose that a recent poll found that 53​% of adults believe that the overall state of moral values is poor.

​(a) For 300 randomly selected​ adults, compute the mean and standard deviation of the random variable​ X, the number of adults who believe that the overall state of moral values is poor.

The mean of X is _________.​ (Round to the nearest whole number as​ needed.)

The standard deviation of X is ________. ​(Round to the nearest tenth as​ needed.)

Answer 1

Solution:

We are given n = 300, p = 0.53, q = 1 – p = 1 – 0.53 = 0.47

Mean = n*p = 300*0.53 = 159

SD = sqrt(n*p*q) = sqrt(300*0.53*0.47) = 8.644652

The mean of X is 159.

The standard deviation of X is 8.6