Unit 3 Chapter 7: Lesson 7.7 Assignment
Score: $49 / 100 \quad 8 / 17$ answered
Question 10
In an election, suppose that $45 \%$ of voters support creating a new fire district. If we poll 143 of these voters at random, the probability distribution for the proportion of the polled voters that support creating a new fire district can be modeled by the normal distibution pictured below. Complete the boxes accurate to two decimal places.
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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. \(\boxed{\text{Mean} = 0.45, \text{Standard Deviation} = 0.042}\)