Question

In a recent survey 75 of the community favored building a police substation in their neighborlhood. If 20 citizens are chosen. What is the mean and standard deviation favoring the substation?

Answer 1

Answer:

Mean = 15

Standard deviation = 1.94

Step-by-step explanation:

We are given the following information:

We treat favoring of building a police substation as a success.

P(Success) = 75% = 0.75

Then the number of citizens follows a binomial distribution, where

$P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}$

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 20

We have to find the mean and the standard deviation.

$\mu = np = 20(0.75 ) = 15\\\sigma = \sqrt{np(1-p)} = \sqrt{20(0.75)(1-0.75)} = 1.94$

Thus, the mean of favoring the substation is 15 and the standard deviation of favoring substation is 1.94