Step 1 :The question is asking for the probability distribution of the proportion of polled voters that support creating a new fire district. Since the distribution is normal, we can use the properties of a normal distribution to solve this problem.
Step 2 :The mean of the distribution is the true proportion of voters that support the initiative, which is 0.45.
Step 3 :The standard deviation of the distribution can be calculated using the formula for the standard deviation of a proportion, which is \(\sqrt{p(1-p)/n}\), where p is the proportion and n is the number of samples. In this case, p = 0.45 and n = 143.
Step 4 :Substituting the values into the formula, we get the standard deviation as approximately 0.042.
Step 5 :Final Answer: The probability distribution can be modeled by a normal distribution with a mean of 0.45 and a standard deviation of 0.042. \(\boxed{\text{Mean} = 0.45, \text{Standard Deviation} = 0.042}\)