what the solution?

Question

Twenty-eight percent of adults contribute to charitable agencies on a regular basis. Let x be the number of adults in a random sample of 18 adults who contribute to charitable agencies on a regular basis. Find the mean and standard deviation of the probability distribution of x.

Answer 1

28% of the sample are expected to contribute to charities, 0.28×18=5.04. This is the mean.

To find the standard deviation, we need to consider the probability of non-contribution=1-0.28=0.72.

The variance is 5.04×0.72=3.63 approx. The standard deviation is the square root of variance=1.9 approx.