Answer:
The mean number of houses burglarized , in an urban area, is 1.
Step-by-step explanation:
Let X = A house in an urban area will be burglarized.
The probability that a house in an urban area will be burglarized is:
P (X) = p = 0.05
The sample size of the houses selected is, n = 20.
The random variable X follows a Binomial distribution with parameters n = 20 and p = 0.05.
The probability function of a Binomial distribution is:
[tex]P(X=x) = {n\choose x}p^{x}(1-p)^{n-x}[/tex]
The expected value of a Binomial distribution is:
[tex]E(X) = np[/tex]
Compute the expected number of houses burglarized as follows:
[tex]E(X) = np=20\times0.05=1[/tex]
Thus, the mean number of houses burglarized , in an urban area, is 1.
