Questions: In an election, suppose that 60% of voters support creating a new fire district. If we poll 139 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 distribution pictured below. Complete the boxes accurate to two decimal places.

In an election, suppose that 60% of voters support creating a new fire district. If we poll 139 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 distribution pictured below. Complete the boxes accurate to two decimal places.

Transcript text: In an election, suppose that $60 \%$ of voters support creating a new fire district. If we poll 139 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.

Solution

Solution Steps

Step 1: Identify the given information

Proportion of voters supporting the new fire district (p) = 0.60
Sample size (n) = 139

Step 2: Calculate the mean of the sampling distribution

The mean (μ) of the sampling distribution of the sample proportion is equal to the population proportion (p). $\mu = p = 0.60$

Step 3: Calculate the standard deviation of the sampling distribution

The standard deviation (σ) of the sampling distribution of the sample proportion is calculated using the formula: $\sigma = \sqrt{\frac{p(1-p)}{n}}$ $\sigma = \sqrt{\frac{0.60 \times 0.40}{139}}$ $\sigma = \sqrt{\frac{0.24}{139}}$ $\sigma = \sqrt{0.001726}$ $\sigma \approx 0.04154$