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
[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]
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.
[tex]\mu = np = 20(0.75 ) = 15\\\sigma = \sqrt{np(1-p)} = \sqrt{20(0.75)(1-0.75)} = 1.94[/tex]
Thus, the mean of favoring the substation is 15 and the standard deviation of favoring substation is 1.94
